what's the derivative of sin(x^3)?

Question

i had it as 3(sinx)^2 times cos(x) and it says (online assignment) that it's wrong...is there some theorem i'm not taking into account?

Answer 1

You've calculated the derivative of (sin x)^3, not sin (x^3).

The derivative of sin (x^3) is cos(x^3) . (3x^2) by the chain rule: let f(x) = sin x, g(x) = x^3. Then we want d/dx (fog)(x) = f'(g(x)).g'(x) = cos(x^3).(3x^2).
You calculated d/dx (gof)(x) = g'(f(x)).f'(x) = 3(sin x)^2.cos x.

Answer 2

if the x^3 is inside the sin, then its just chain rule

so (3x^2)(cos(x^3))