Find the derivative of x-3 (5 + 3x)

By Leibnitz product rule,

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

\( x^{-3}(0+3)+(5+3x)(3x^{-3-1})\)

\( x^{-3}(3)+(5+3x)(3x^{-4})\)

\(3x^{-3}-15x^{-4}-9x^{-3}\)

\( -6x^{-3}-15x^{-4}\)

\(\dfrac{-3x^{-3}}{x}(2x+5)\)

\( \dfrac{-3}{x^4}(5+2x)\)