Show that the gradient of y = (x^2 – 1)(x – 2)^3 is given by dy/dx= (x-2)^2(5x^2-4x-3)

Question

differentiation.

Answer 1

Given...y=(x^2-1)(x-2)^3

let....u=(x^2-1)

       V=(X-2)^3

du/dx=2x

dv/dx=3(x-2)^2

by appliying product rule                                                                                                                     
dy/dx=vdu/dx+udv/dx

=2x(x-2)^3+3(x^2-1)(x-2)^2

=(x-2)^2{2x(x-2)+3(x^2-1)}

=(x-2)^2{2x^2-4x+3x^2-3}

=(x-2)^2{5x^2-4x-3}