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!