F(x)=(x^(2) )/(x+1) Find the derivative of f(x) by using first principles.

Question

`f(x)=(x^(2) )/(x+1)`

Find the derivative of
`f(x)` by using first principles.

Answer 1

Explanation:

which of the principles and the question is not clear i saw something different before i clicked on it

Answer 2

`(x^2 + 2x)/((x + 1)^2)`

Explanation:

`f(x) = (x^2)/(x + 1)`

`(d)/(dx) (x^2)/(x + 1) =`

`= (d)/(dx) [(x^2)(x + 1)^(-1)]`

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

`= (-x^2)/((x + 1)^(2)) + (2x)/(x + 1)`

`= (-x^2)/((x + 1)^(2)) + (2x^2 + 2x)/((x + 1)^2)`

`= (x^2 + 2x)/((x + 1)^2)`