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

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Answer 1 · 2018-07-04T12:36:24

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

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#