Question

What is the derivative of `sin^5(x)`?

Answer 1

`5sin^4xcosx`

Explanation:

differentiate using the `color(blue)"chain rule "`

`color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))........ (A)`

let `y=sin^5x=(sinx)^5`

let `u=sinxrArr(du)/(dx)=cosx`

and `y=u^5rArr(dy)/(du)=5u^4`

substitute these values into (A) convert u back to x

`rArrdy/dx=5u^4(cosx)=5sin^4xcosx`