Question

What is the derivative of `1/(x+1)`?

Answer 1

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

Explanation:

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

and using the `color(blue)(" chain rule ")`

`d/dx(f(g(x)) = f'(g(x)) . g'(x)`

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

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