Derivative of a quotient

\left(\tfrac{f}{g}\right)'=\dfrac{f'g-fg'}{g^2}

Result unit: — (funkcja)

What it describes

The rule for differentiating a quotient of two functions (when

g\neq 0

f, g

functions (

g\neq 0

)

The quotient rule — "bottom times derivative of top minus top times derivative of bottom, all over bottom squared".

Differentiating rational functions and quotients.

Find the derivative of

\dfrac{x}{x+1}

Substitution

f=x

g=x+1

Result

\dfrac{1\cdot(x+1)-x\cdot1}{(x+1)^2}=\dfrac{1}{(x+1)^2}

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