Question

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

Answer 1

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

Explanation:

You could write `f(x)=1/(x+1)=(x+1)^{-1}` and use the power rule and chain rule: `f'(x)=(-1)(x+1)^(-2) * d/dx(x+1) = -1(x+1)^(-2) * 1 = -1/(x+1)^2`.

You could also use the quotient rule:

`f'(x)=((x+1) * d/dx(1) - 1 * d/dx(x+1))/((x+1)^2)=(0 - 1)/((x+1)^2) = -1/(x+1)^2`