Differentiate with respect to x the function below: (x)/(x+1)

Question

Differentiate with respect to x the function below:
`(x)/(x+1)`

Answer 1

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

Explanation:

Differentiate using the Quotient rule.

Given

y =
`(f(x))/(g(x))` , then

`(dy)/(dx)` =
`(g(x)f'(x)-f(x)g'(x))/((g(x))^2)`

Here

y =
`(x)/(x+1)` , with

f(x) = x ⇒ f'(x) = 1

g(x) = x + 1 ⇒ g'(x) = 1

Thus

`(dy)/(dx)` =
`((x+1).1-x.1)/((x+1)^2)`

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

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