Chapter 2 - The Derivative - 2.4 The Product And Quotient Rules - Exercises Set 2.4 - Page 147: 7

$f'(x)=-15x^{-2}-14x^{-3}+48x^{-4}+32x^{-5}$

Take the derivative of the equation using Product Rule and simplify: $f'(x) = (x^3+7x^2-8)(-3*2x^{-4}-4x^{-5})+(3x^2+2*7x^1-0)(2x^{-3}+x^{-4})$ $=(x^3+7x^2-8)(-6x^{-4}-4x^{-5})+(3x^2+14x)(2x^{-3}+x^{-4})$ $=(-6x^{-1}-42x^{-2}+48x^{-4}-4x^{-2}-28x^{-3}+32x^{-5})+(6x^{-1}+28x^{-2}+3x^{-2}+14x^{-3})$ $=-15x^{-2}-14x^{-3}+48x^{-4}+32x^{-5}$