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

1 Answer

Dec 19, 2015

#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#

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