Question

Calc 1: dy/dx (e^y)(cosx)
I got (e^y)(-sinx) + (cosx)(e^y), but I feel I'm missing something.

Answer 1

This is implicit differentiation. If this were e^x(cosx) then this would be e^x(cosx) -e^x(sinx) which is of the same form of your solution.

Hint: When you take the derivative of e^y it is (e^y)y'

Answer 2

Yes, u = e^y -> u' = y' e^y
v = cosx -> v' = ..

Answer 3

Thank you, That's what I thought, but could you explain why because I'm still a little confused.

Answer 4

Y is function of x, so when you take dy/dx ( with respect to x): chain rule need to be applied for y!