Question

What is the derivative of `f(x)=e^sinx - cos(e^x)`?

Answer 1

I found: `f`(x)=e^(sin(x))cos(x)+e^xsin(e^x)`

Explanation:

Here I would use the Chain Rule to deal with the function of a function as in `e^(sin(x)` and `cos(e^x)` by deriving the first one (in red) and then multiplying by the derivative of the second (in blue):

`f`(x)=color(red)(e^(sin(x)))*color(blue)(cos(x))-(color(red)(-sin(e^x))*color(blue)(e^x))=`

`=e^(sin(x))cos(x)+e^xsin(e^x)`