Question

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

Answer 1

`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`