# Thread: Exponential derivative (cos/sin)

1. ## Exponential derivative (cos/sin)

Im strugging through calc I after being away from school for 12 years, so some of the more basic functions are giving me fits. The chain rule makes sense to me, but I'm struggling with some of the more basic applications.

The problem I am trying to solve is ln(x)^cosx

I am just stuck on where to go after step 1, which is the first chain 1/x^cosx. What is the next derivative before the last, which would be -sinx?

Thanks!

2. ## Re: Exponential derivative (cos/sin)

Originally Posted by Russell
The chain rule makes sense to me, but I'm struggling with some of the more basic applications.
The problem I am trying to solve is ln(x)^cosx
You have not stated a problem clearly.
Are you required to find the derivative of
$f(x)=\ln(x)^{\cos(x)}~?$

3. ## Re: Exponential derivative (cos/sin)

Oh I realized that I didn't say I needed the deriv of that...yes that is correct. Sorry

4. ## Re: Exponential derivative (cos/sin)

Originally Posted by Russell
Oh I realized that I didn't say I needed the deriv of that...yes that is correct.
Let $\ln(y)=\cos(x)\ln(\ln(x))$. Now use implicit derivatives and then solve for $y'~.$