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Find a formula for the derivative of a given function

by RoRi

Find a formula for the derivative of the function

    \[ f(x) = \frac{1}{x+1} \qquad x \neq -1. \]

Using the formula for the derivative of a quotient, we have,

    \[ f'(x) = \frac{(1)'(x+1) - 1 (x+1)'}{(x+1)^2} = - \frac{1}{(x+1)^2} \qquad \text{for } x \neq -1.\]

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