Question

find the derivative of y=sin^3 x

Answer 1

What you want to remember here is the chain rule. Take each part by itself.
=sin^3(x)
= 3sin^2(x) = 3cos^2(x)*1 = 3cos^2(x)
Remember the 1 from the inner x, if it's something else then x it could change the result.
Unless I'm forgetting the chain rule myself, but it should be correct. :)

Answer 2

THANK YOU :)

Answer 3

You're welcome :)

Answer 4

This is incorrect. The inner function is \[f(x) = \sin{x}\] and the outer function is \[g(x) = x^{3}\] Thus \[\frac{d}{dx} \sin^3{x} = \frac{d}{dx} g \circ f = \frac{dg}{dx}(f(x)) \cdot \frac{df}{dx} = 3\sin^2{x} \cdot \cos{x} \]

Answer 5

Yeah, thought I did something wrong. Good catch!