Find the derivative of x-4 (3 – 4x-5)

By Leibnitz product rule,

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

\( x^{-4}\{(0-4(-5)x^{-5-1}\}+(3-4x^{-5})(-4)x^{-4-1}\)

\( x^{-4}(20x^{-6})+(3-4x^{-5})(-4x^{-5})\)

\( 20x^{-10}-12x^{-5}+16x^{-10}\)

\( 36x^{-10}-12x^{-5}\)

\( \dfrac{12}{x^{-5}}+\dfrac{36}{x^{10}}\)