Find the derivative of the following functions (it is to be understood that x^4(5sinx-3cosx)

Let f(x) = \( x^4(5sinx-3cosx)\)

By product rule,

\( f'(x)=x^4\dfrac{d}{dx}(5sinx-3cosx)\)

\( +(5sinx-3cosx)\dfrac{d}{dx}(x^4)\)

\(x^4[5\dfrac{d}{dx}(sinx)-3\dfrac{d}{dx}(cosx)]\)

\( +(5sinx-3cosx)\dfrac{d}{dx}(x^4)\)

\( x^4[5cosx-3(-sinx)]+(5sinx-3cosx)(4x^3)\)

\( x^3[5xcosx+3xsinx+20sinx-12cosx]\)