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

1 Answer
Jul 4, 2018

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