Question

What is the derivative of `sin^3(x)cos(x)`?

Answer 1

`d/dx(sin^3xcosx)=-sin^4x+3sin^2xcos^2x`

Explanation:

Here We use: Product Rule , Power Rule and Differentiation of Trigonometric Functions

`color(green)(d/dxsinx=cosx`

`color(green)(d/dxcosx=-sinx`

`d/dx(sin^3xcosx)=sin^3xd/dx(cosx)+cosx*3sin^2xd/dx(sinx)`

`d/dx(sin^3xcosx)=sin^3x*(-sinx)+3cosx*sin^2x*cosx`

`d/dx(sin^3xcosx)=-sin^4x+3sin^2xcos^2x`