Question

Using implicit differentiation, find f' of y=sin(x+y).

Answer 1

( sin u)' = ...?

Answer 2

Sorry?

Answer 3

Let u be (x+y), what would the derivative of \(\large \sin(u)\) be?

Answer 4

cos(x+y)

Answer 5

Alright, now you'll have to apply the chain rule, so it would give \(\large \sin(u)u'\).

Answer 6

cos(x+y)(x+y)'.. but now what? That's where I'm stuck.

Answer 7

u = x + y --> u' = x' + y' = 1 + y'

Answer 8

Is the answer y'=cos(x+y)(1+y) then? :$

Answer 9

cos(x+y) + cos(x+y) y' would be the answer.