# Thread: Derivative of exponential function

1. ## Derivative of exponential function

(x+cot (x))^sin (x^2)

I tried solving the problem by taking a log with base (x+cot (x))
Is it acceptable to take a log with a variable base ??
If not, please I would have the solution of the problem.

Thanks in advance !!

2. Originally Posted by egt2010
(x+cot (x))^sin (x^2)

I tried solving the problem by taking a log with base (x+cot (x))
Is it acceptable to take a log with a variable base ??
If not, please I would have the solution of the problem.

Thanks in advance !!

Since $a^b=e^{b\ln a}$ , we get $(x+\cot x)^{\sin x^2}=e^{\sin x^2\ln (x+\cot x)}$. Apply now the chain rule.

Tonio