How do you use the chain rule to differentiate (sinx)^10?

1 Answer
Nov 5, 2016

(dy)/(dx)=10sin^9xcosx

Explanation:

By treating (sinx)^10 as a function in terms of sinx, and sinx as a function in terms of x, chain rule can be applied where:

(dy)/(dx)=(dy)/(du)*(du)/(dx)

Let u=sinx

:.y=u^10

(dy)/(du)=10u^9=10(sinx)^9

(du)/(dx)=cosx->the derivative of sinx is cosx

:.(dy)/(dx)=10(sinx)^9*cosx=10sin^9xcosx