Quotient Rule

The rule

For a quotient of two functions, "low d-high minus high d-low, over low squared":

Worked example

Differentiate $y = \dfrac{2x+1}{3x-4}$.

Solution: With $u=2x+1$ ($u'=2$) and $v=3x-4$ ($v'=3$):

A function's derivative at a point

The functions $f(x)$ and $g(x)$ are differentiable, and $h(x) = \dfrac{g(x)}{f(x)}$. Given $f(0)=-7$, $f'(0)=5$, $g(0)=3$, and $g'(0)=-6$, find $h'(0)$.

Solution: By the quotient rule, $h'(x) = \dfrac{g'(x)f(x) - g(x)f'(x)}{f(x)^2}$. Substituting the values at $x=0$: