Math Help - Trigonometric Derivative

1. Trigonometric Derivative

What is the derivative of $sin^\frac {1}{3} x$?
Actually part of a bigger problem, but I think I can tackle it if I just know this.

2. Originally Posted by seuzy13
What is the derivative of $sin^\frac {1}{3} x$?
Actually part of a bigger problem, but I think I can tackle it if I just know this.
let $t=y^{\frac{1}{3}}$ and $y=\sin x$ we need dt/dx

$dt/dx = dt/dy \cdot dy/dx$

$dt/dx = 1/3y^{\frac{-2}{3}} \cdot \cos x$ sub y value

$dt/dx = 1/3(\sin x)^{\frac{-2}{3}}(\cos x )$

$dt/dx = \frac{\cos x }{3(\sin ^{\frac{2}{3}})}$

that's it