Question

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

Answer 1

Using the chain rule.

Explanation:

• Chain rule states that `(dy)/(dx)=(dy)/(du)(du)/(dx)`

So, as for your function, you can think of each term separately, if you want, renaming `u=cosx` for the first and `v=e^x` for the second and apply the rule, which will end up giving you the following:

`(df(x))/g(x)=sinxe^(cosx)-e^xsin(e^x)`