Question

Find f '(x) if f(x) = (cos (sin(x^2)))^3

Answer 1

-6.x.cos(x^2).sin(sin(x^2)).(cos(sin(x^2))^2

Answer 2

We'll use chain rule to differentiate with respect to x:
f'(x) = 6x*(cos(sin x^2))^2*(-sin(sin x^2))*(cos x^2)

Answer 3

can you explain the chain rule to me? Im so confused with that area

Answer 4

isnt it -6? O.o Is that a mistake ? :P

Answer 5

I may be wrong lol

Answer 6

we consider the given function as a result of composition of 4 functions. the power function (cosine raised to cube), then cosine function, sine function and the monomial x^2.
You'll have to differentiate each function with respect to x.

Answer 7

yes -6

Answer 8

yes, -6

Answer 9

Thank you!

Answer 10

No, no no. Thank YOU!