Question

Hey guys I have a couple questions.

What is the derivative of the function f(x)=[e^(-x)]cosx?
And y=ln(tan x), y'=???

Answer 1

The first one(if i solved it correctly):
-Rewrite It: f(x) = (1/e^x) * cos(x)
Using the product rule: y'=(-1/e^2x)*e^x * cos(x) - sin(x)/e^x [Remember chain rule for 1/e^x]
And finally: \[y'=(-e^{-x}) (\cos(x) + \sin(x) )\]