# Thread: differentiate f(x) using chain rule (i think?)

1. ## differentiate f(x) using chain rule (i think?)

Differentiate the function. You do not need to simplify your answer

f(x)=sin(cos3x)+cos(5sinx)

i thought in order to go about doing this you had to usethe chain rule for
each component

d/dx(sin(cos3x))+d/dx(cos(5sinx))

d/dx(sin(cos3x))
using chain rule = cos(cos3x)* -sin3x

d/dx(cos(5sinx))
using chain rule = -sin(5sinx)* 5cosx

so f '(x) = [cos(cos3x)* -sin3x] + [-sin(5sinx)* 5cosx]

all this is a new concept just recently learned in my math class, and i really don't know what i'm doing. hopefully i'm somewhat on the right track??
thanks in advance!

2. Don't forget to go all the way down to "x". When you differentiate "cos(3x)", you differentiate the cosine, and then the 3x!

. . . . . $\frac{d(\sin{(\cos{(3x)}})}{dx}\, =\, \cos{(\cos{(3x)})}\,\times\, \-\sin{(3x)}\,\times\,3$