Question

What is the derivative of `f(x)=3sin^2x`?

Answer 1

`f'(x)=3sin2x`

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

note : `sin^2x=(sinx)^2`

so `y=3u^2rArr(dy)/(du)=6u`

substitute these values into (A) changing u back into terms of x.

`rArrdy/dx=6ucosx=6sinxcosx`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(sin2x=2sinxcosx)color(white)(a/a)|)))`

`rArrdy/dx=6sinxcosx=3sin2x`