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quotient rule

The rule for differentiating a ratio of two functions.

For $f(x)=\dfrac{u(x)}{v(x)}$ , $f'(x) = \dfrac{u'(x)v(x)-u(x)v'(x)}{[v(x)]^2}$ , valid wherever $v(x)\neq0$ .

Examples

For $f(x)=\dfrac{x}{x+1}$ : $f''(x)=\dfrac{1\cdot(x+1)-x\cdot1}{(x+1)^2}=\dfrac{1}{(x+1)^2}$ .