Question

If `y=sin^5x` then what is `dy/dx`?

Answer 1

Use the chain rule

Explanation:

If `y=sin^5x`, then Let `u=sin x`,

Then `(du)/(dx)=cosx` and `y=u^5` so `(dy)/(du)=5u^4`

Chain rule gives `(dy)/(dx)=(dy)/(du) (du)/(dx)`. so:
`(dy)/(dx)= 5u^4 cosx = 5sin^4x cos x`