A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
fine i am puttin ma questions here
anonymous
 5 years ago
fine i am puttin ma questions here

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01st of all in the question \\[y = sinx ^{x ^{2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here i could not understand i got till \[d/dx(\log y) = d/dx(x^2 \log (\sin x))\] but am not able to proceed further

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The chain rule states that, \[d/dx(f(y)) = f'(y) dy/dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok lets go slowly. your problem is that the variable is in the exponent. you get it out of the exponent by taking the log

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so first step is to take the log

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now d/dx(logy) = 1/y dy/dx? Did you get this?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no amogh i did not get this !!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[ln(sin(x))^{x^2}=x^2ln(sin(x))\] by the properties of logs

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that's wat i did till here i got !!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0satellite: I suggest you to start using a basic chain rule example as he stumbles only upon the chain part! good luck

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok next step is to take the derivative. \[\frac{d}{dx}x^2ln(sin(x))\] and for this you need both the product rule and the chain rule.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0dude i did this already!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so now i apply chain rule????????

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0as it is both a product, \[x^2\times ln(sin(x))\] and \[ln(sin(x))\] is a composite function. is the the log OF the sine of x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wat do u mean by a composite function??????

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in english, the derivative of a composite function is the derivative of the outside function evaluated at the inside function, times the derivative of the inside function.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0composite means \[f(g(x))\] so if \[f(x)=ln(x)\] and \[g(x) = sin(x)\] then \[f(g(x))=ln(g(x))=ln(sin(x))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wat happened to the outer x^2????

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when i diff (log y )i get i/y

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is a composition of functions. another example. \[f(x)=\sqrt{x}\] \[g(x)=1x^2\] \[f(g(x))=f(1x^2)=\sqrt{1x^2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh no. the derivative of \[ln(x)=\frac{1}{x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am saying the same for th LHS ie log y

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but the derivative of \[ln(g(x))=\frac{1}{g(x)}\times g'(x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the derivative of \[ln(sin(x))=\frac{1}{sin(x)}\times cos(x)=\frac{cos(x)}{sin(x)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am going slow and still wanting to take the derivative of \[x^2ln(sin(x))\] correctly. we will deal with the consequence of taking the log later.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes here is where i am stuck

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0x^2 becomes 2x right???????

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you have a product here. do you know the product rule?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yay so we get in the end 2x.(ln(sin(x)))

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0product rule says dat 1st take the 1st constant and diff the other and add the vis  a  vis to it!!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nope sorry. again lets to slow

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0CHEATING!!!!!!! ( cranky kid's voice)!!!!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the derivative of \[f(x)g(x)\] is \[f'(x)g(x)+g'(x)g(x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well dat's wat i said in words just to avoid the typing!!!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0put \[f(x)=x^2\] \[f'(x)=2x\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[g'(x)=\frac{cos(x)}{sin(x)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now dis is de place where i get stuck up y do we get dis????????????

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ahh that is the "chain rule"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i say it in english. the derivative of log x is one over x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how is this the chain rule i mean i just read it for algebra not for log or sin

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but the derivative of log of "something" is one over something times the derivative of " something"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so by dat logic ln(sin(x) ) when derivatived we shud get 1/sin(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0times the derivative of sine(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know the derivative of sin(x)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i know dat u r a gud teacher and u r real patient thanx for dat!!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so i repeat but the derivative of log of "something" is one over something times the derivative of " something"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we multiply the cos(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok ca we quickly repeat!!!!!!!!!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we get the derivative of \[ln(sin(x))\] is \[\frac{1}{sin(x)}\times cos(x)=\frac{cos(x)}{sin(x)}\]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we get 1/y = 2x. cos(x)/sin(x) true???

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0srsly whew my brain is alrdy stewd!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now we put this all back in the product rule (FG)'=F'G+G'F \[F+x^2\] \[F'=2x\] \[G=ln(sin(x))\] \[G'=\frac{cos(x)}{sin(x)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes go on!!!!! i am trying to get a full pic

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0to get .... the derivative of \[x^2ln(sin(x))=2xln(sin(x))+x^2 \frac{cos(x)}{sin(x)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that is the product rule, although we used the chain rule to find the derivative of \[ln(sin(x))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0whew. of course we are not done! believe it or not. because we took the log as the first step

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i cud not pick that up!!!!! that ln(sin(x) ) was by a rule??????????

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we did not find the derivative of the original thing, we found the derivative of the log of the original thing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i will say quickly what we do next because it is easy. then i will give an explanation. next we simply get our answer by multiplying what we got above by the original function. done.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0CONFUSION HERE IN WAT U JUST SAID (short circuited)!!!!!!!!!!!!!!!!!!!!!!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0answer is... \[(sin(x))^{x^2}\times (2xln(sin(x))+\frac{x^2cos(x)}{sin(x)})\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the first part is the original function you were to differentiate. the second part was the derivative of the log of that good luck

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i can 't understand the final step on how to obtain the answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok final step. don't forget that the first step was taking the log. so we took the derivative of \[ln(f(x))\] not \[f(x)\] by the chain rule the derivative of \[ln(f(x))\] is \[\frac{1}{f(x)}\times f'(x)=\frac{f'(x)}{f(x)}\] that is \[\frac{d}{dx}ln(f(x))=\frac{f'(x)}{f(x)}\] solving this equation for \[f'(x)\] gives \[f'(x)=f(x)\times \frac{d}{dx}ln(f(x))\] in english you can find the derivative by first taking the log of your function, then differentiating the log of your function, and then multiplying by the original function. hope this helps
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.