Question

diffferentiate the following w.r.t. x: (5x^2-x^7)(20x^2+3x^-7)​

Answer 1

By Quotient rule,

dy/dx = [ (10x - 7x^6)(20x^2+3x^-7) - (5x^2-x^7)( 40x - 21 x^(-8))] / (20x^2+3x^-7)^2

dy/dx = [ (200x^3 + 30x^-6 - 140x^8 - 21x^-1) - (200 x^3 - 105 x^-6 - 40x^8 + 21 x^-1)] / (20x^2+3x^-7)^2

dy/dx = (135 x^-6 - 100 x^8 - 42 x^-1) / (20x^2+3x^-7)^2