Question

What is the derivative of `cosx^3`?

Answer 1

`-3x^2sinx^3`

Explanation:

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(f(g(x)))=f'(g(x)).g'(x))color(white)(a/a)|))....(A)`

`f(g(x))=cos(x^3)rArrf'(g(x))=-sin(x^3)`

and `g(x)=x^3rArrg'(x)=3x^2`
`"----------------------------------------------------"`
Substitute these values in `color(red)"(A)"`

`rArrd/dx(cosx^3)=-sinx^3 .3x^2=-3x^2sinx^3`