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

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Answer 1 · 2015-12-19T03:38:59

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

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:

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

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