Differentiate the following w.r.t. x:
`log(cose^x)`

Explanation

To differentiate the function \( \log(\cos(e^x)) \) with respect to \( x \), we will use the chain rule. Here’s a step-by-step solution:

### Step 1: Identify the outer and inner functions
The function \( \log(\cos(e^x)) \) can be seen as a composition of functions:
- Outer function: \( f(u) = \log(u) \) where \( u = \cos(e^x) \)
- Inner function: \( g(v) = \cos(v) \) where \( v = e^x \)
- Innermost function: \( h(x) = e^x \)

...