Question

Differentiation of cos cube x?

Answer 1

Shown below...

Explanation:

Use the chain rule:

`d/dx f( g(x) ) = g'(x) * f' (g(x) )`

In this case `d/dx cos^3 x = d/dx (cosx)^3`

`=> f(x) = x^3` and `g(x) = cosx`

Use `d/dx cosx = -sinx`

`=> d/dx cos^3 x = 3 * cos^2 x * (-sinx )`

`=color(red)( -3sinxcos^2 x`