How to find the derivative of `e^{cos(8t)+ln(t)}` 

Expert Answers
lfryerda eNotes educator| Certified Educator

In order to find the derivative of this function, we need to know the derivatives of `(cos x)'=-sin x` , `(e^x)'=e^x` and `(ln x)'=1/x` .  In addition, we need to be able to use the chain rule.  When you take the derivative of a function, you need to multiply the derivative by the derivative of the argument of the function.  So, for the derivative of `cos8x` , we need to multiply by the derivative of `8x` , which is 8.

This means we get:

`(e^{cos(8t)+ln(t)})'`   take derivative of arguments and multiply.


The derivative is `e^{cos(8t)+ln(t)}(-8sin(8t)+1/t)` .