# if h and k are functions of x, then what is the derivative of h/k

## Question:

If **h** and **k** are functions of **x**, then what is the derivative of {eq}\frac{h}{k} {/eq}

## Quotient Rule:

If the function {eq}g(x) {/eq} equals the ratio {eq}\displaystyle \frac {u(x)}{v(x)} {/eq} of two functions {eq}u {/eq} and {eq}v {/eq} of {eq}x {/eq}, the first derivative of {eq}g(x) {/eq} with respect to {eq}x {/eq} can be obtained using the quotient rule of differentiation:

{eq}\displaystyle \left(\frac {u}{v}\right)^{'}=\frac {vu^{'}-vu^{'}}{v^2} {/eq}

## Answer and Explanation:

Since {eq}h {/eq} and {eq}k {/eq} are functions of the variable {eq}x {/eq}, per the quotient rule of differentiation, the derivative of the...

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