# Quotient Rule Calculator

Quotient rule calculator: The quotient rule can be used to find the derivative of a function’s ratio of two differentiable functions.

Let f(x)=g(x)/h(x), where both g and h are differentiable and h(x)≠0.

The quotient rule states that if {\displaystyle \frac{f}{g}=\frac{k}{h}, } then,

Discovered by Gottfried Wilhelm Leibniz in 1676, this is also known as Leibniz’s Rule or simply the quotient law. Read about: Product Rule

## Quotient Rule Calculator

It follows directly from the product rule for derivatives:

let u=g(u)/h(u) be divided by v=g(v)/h(v). Then,

du/dv= (u/v)·(du/dg)(dg/dh),

### or, in symbols,This can also be written as

Where the limit as h→0 is taken.

In other words, the derivative of a quotient is the product of the derivatives of the numerator and denominator, evaluated at the point where the denominator is zero.

This allows you to find this derivative without going through all of the algebra.

Just enter in the functions for g and h and the point at which you want to find the derivative, and the calculator will take care of the rest.

Quotient rule calculator is a tool to find derivative of function f(x) where g(x)/h(x), with h≠0.

Enter any three known values into X, Y, Z and click ‘Calculate’.

Values entered: • f = x²/y • g = sin(x) • h = cos(2x)