What the quotient rule says
Differentiating a fraction needs care with the minus sign. The identity (f/g)′ = (f′g − fg′) / g² is the standard quotient rule. This quotient rule calculator applies it with labeled steps so you can audit the numerator order and the squared denominator.
A mnemonic many courses use: “low d-high minus high d-low, over low squared.” Match that chant to the step list after each run.
How to use this quotient rule derivative calculator
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Enter a quotient with parentheses, e.g.
(x^2+1)/(x-1). - Press Calculate and find the quotient-rule step.
- Check the sign between the two numerator terms.
- Confirm the denominator is the original bottom squared before simplifying.
Quotient rule practice set
(x^2+1)/(x-1)— polynomial over linear(x+1)/(x-1)— classic rational warm-upsin(x)/x— trig over linear (sinc-related)x/(x^2+1)— linear over quadratic(e^x)/(x+1)— exponential numerator(x^2)/(3*x+2)— power over linear
Quotients mixed with chain or product
Numerators or denominators that are compositions pull in the chain rule inside the quotient pattern. If your expression is better seen as a product, try the product rule calculator. Pure compositions belong on the chain rule calculator.
After you have f′(x), evaluate at a point with the derivative at a point workflow, or raise Order on the second derivative calculator for complicated rational second derivatives.
Quotient rule calculator FAQ
What is the quotient rule?
(f/g)′ = (f′g − fg′) / g². Watch the minus sign and square the denominator.
How do I use this calculator?
Type a fraction with clear parentheses, Calculate, and read the labeled quotient steps.
Is it free?
Yes — free steps with no account or Pro wall.
Can I use a product of f and 1/g instead?
Often yes. This page keeps the classic quotient form that many courses require.