Question

What is the derivative of `f(x)=secx^2e^(xcosx)`?

Answer 1

`f=sec x^2, g = e^(xcosx)->f'=secx^2tanx^2*2x,g'=e^(xcosx)*(-xsinx+cosx)`
`f'(x)=fg'+gf'=(secx^2)e^(xcosx)(-xsinx+cosx)+e^(xcosx)(2xsecx^2tanx^2)`

Explanation:

Use the product rule. Separate the two functions into f and g and then find f' and g' separately. Note that you will have to use the chain rule to find derivatives of f and g. Once you have f' and g' put it into the product rule and simplify.