How do you differentiate f(x)=(2x+3)^4 / x using the chain rule?

1 Answer
Jul 21, 2016

d/dx (f(x)) = d/dx ((2x+3)^4/x)
Or, f'(x) = 1/x * d/(d(2x+3)) (2x+3)^4* d/dx (2x+3) + (2x+3)^4 d/dx (1/x)
=1/x * 4 (2x+3)^3 * 2- (2x+3)^4/x^2
=(8x (2x+3)^3-(2x+3)^4)/x^2
=(2x+3)^3(8x-2x-3)/x^2
= 3 (2x+3)^3 * (2x -1) / x^2