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600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:12:02 | how did you find that? | 1 | 0 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:12:10 | or is it because there is no answer | 1 | 0 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 200,013,547,491,688,450 | a disappointing son | 02/09/2022 14:12:17 | 1x^2=x^2 | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 200,013,547,491,688,450 | a disappointing son | 02/09/2022 14:12:27 | the ? you wrote is just an imaginary 1 | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 200,013,547,491,688,450 | a disappointing son | 02/09/2022 14:12:31 | we just don't write it cause there's no point | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 200,013,547,491,688,450 | a disappointing son | 02/09/2022 14:12:33 | x*1=x | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:12:39 | ah ok | 1 | 0 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:13:04 | is a ever a number apart from 1 then? | 1 | 0 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:13:16 | or is it always 1 | 1 | 0 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 200,013,547,491,688,450 | a disappointing son | 02/09/2022 14:14:03 | it could be something other than 1 | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 200,013,547,491,688,450 | a disappointing son | 02/09/2022 14:14:12 | say you were given x=2/3 and x=5 as your roots | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 200,013,547,491,688,450 | a disappointing son | 02/09/2022 14:14:32 | ,w expand (3x-2)(x-5) | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 510,789,298,321,096,700 | TeXit | 02/09/2022 14:14:36 | Results provided by WolframAlpha | 0 | 1 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:14:45 | ah ok | 1 | 0 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:15:19 | thanks man you have really helped | 1 | 0 | null | null | null | null | null | |||||
600 | help-10 | 72253de5a4e649169f69e88a387aa70f | 649,650,500,479,746,000 | Yi long mu | 02/09/2022 14:18:50 | .close | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:21:23 | Can anyone walk me through this? | unknown.png | 1 | 0 | null | null | null | null | null | ||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:22:24 | I know for pi(sin(u)) it is pi(cos(u)) but how about the -2^u? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:30:42 | write 2^u as e^(ln(2) * u) | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:31:44 | Alright | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:32:56 | So then u'/u so would it just become 0/2 * u? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:33:14 | so 0*u | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:33:31 | u' / u? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:33:52 | do you know how to take the derivative of an exponential? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:33:59 | but it is a log | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:34:07 | the log is a constant | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:34:20 | log(2) = const, not dependent on u | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:34:22 | so the log is 0 | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:34:28 | log(2)=0 | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:34:34 | no | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:34:45 | how is it not? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:34:53 | what is the derivative of e^(2x)? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:35:03 | where does that come from? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:35:18 | because you're taking the derivative in the wrong way | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:35:29 | How am I doing it in the wrong way | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:35:35 | you have to use the chain rule | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:35:58 | I am so lost | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:36:10 | . | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:36:46 | now replace the 2 with ln(2), same thing | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:36:47 | but I dont get where that even came from | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:36:59 | you're trying to differentiate the log in the exponent | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:37:08 | but its just a constant number like 2 | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:37:26 | but arent the derivatives of constants 0? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:37:35 | but you have ln(2) * u | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:37:41 | not just ln(2) | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:38:17 | but where does the e come from | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:38:21 | and where does the x come from | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:38:30 | that was just an example | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:38:36 | you can use any letter | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:38:57 | so with ln(2)*u how do you set that up | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:39:16 | wdym? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:39:25 | the derivative of that or where it came from? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:39:41 | how do you set it up to find the derivative of that? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:40:01 | the derivative of ln(2) * u is simply ln(2) | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:40:08 | how? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:40:14 | oh is it because u^1? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:40:14 | factor rule? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:40:28 | and then power rule is u^1-1 | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:40:31 | so u^0? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:40:33 | yes | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:40:36 | Ok | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:40:58 | so then is the answer pi(cos(u))-ln(2)? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:41:05 | nono | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:41:24 | you know that the derivative of e^u is e^u right? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:42:01 | but in our case we have e^(ln(2) * u). we need to apply the chain rule because the exponent is a function of u itself | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:42:23 | this is so confusing | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:42:32 | I thought the u was gone | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:42:35 | the * u | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:42:40 | because it becomes u^0 | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:42:48 | yes the inner derivative becomes ln(2) | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:42:51 | so then we are just left with ln(2) and no * u | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:42:55 | but you also need the outer derivative | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:43:10 | e^(2u) => 2 * e^(2u) | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:43:23 | so you put the u inside the ln? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:43:42 | e^(ln(2) * u) => ln(2) * e^(ln(2) * u) | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:43:43 | I dont get where the e comes from | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:44:11 | because we have rewritten 2^u as e^(ln(2) * u) | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:44:22 | how though? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:44:33 | I dont get how you just do that | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:44:38 | well you know that exp and ln are inverse functions of each other? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:44:57 | why does it have to change around | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:44:59 | I am so lost | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:45:17 | did you learn about exponential derivatives in class? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:45:18 | I am just completely failing to understand what you are saying | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:45:28 | no | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:45:34 | Im trying to right now I guess | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:45:51 | well you have to because otherwise it's not possible to solve | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:46:28 | is it possible to learn how to do that in 15 minutes? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:47:05 | if you know exponent rules and basic differentiation rules, yes | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:47:31 | what should I do to learn it | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:51:57 | Well first you have to know that e^x and ln(x) are inverse functions. So e^(ln(x)) = x and ln(e^x) = x. | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:52:15 | Alright | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:52:23 | so in the case of this problem it becomes e^(ln(2)) | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:52:35 | which means e^(ln(2)) = 2? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:52:37 | Now why did we rewrite 2^u to e^(ln(2) * u)? | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:52:59 | Right | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:53:11 | but you multiply by u as well | 0 | 1 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:53:16 | that is because the u is not included in the inner part of the function | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 855,857,744,590,798,800 | Cherno | 02/09/2022 14:53:28 | so it isnt ln(2u) it is ln(2)*u? | 1 | 0 | null | null | null | null | null | |||||
601 | help-10 | 75a6576e37204ba58d49d1558e08a7db | 392,341,051,794,391,040 | Navix | 02/09/2022 14:54:18 | e^(ln(2) * u) = e^(ln(2))^u | 0 | 1 | null | null | null | null | null |
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