Quotient Rule Calculator
Work out quotient rule instantly with clear inputs, formula shown and shareable results.
About Quotient Rule Calculator
The quotient rule gives (u/v)' = (u'v − uv')/v². The minus sign matters: increasing the denominator decreases the quotient, so its contribution is subtracted.
Formula
Quotient rule
(u/v)' = (u'v − uv') / v²
Worked example
With the default values below, Quotient Rule Calculator returns (u/v)' = (u'v − uv')/v² of 8.43492185. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numeratorone of a·xᵖ, a·sin(kx), a·cos(kx), a·e^(kx), a·ln(kx)
- a·xᵖ
- Denominatorone of a·xᵖ, a·sin(kx), a·cos(kx), a·e^(kx), a·ln(kx)
- a·cos(kx)
- Power p for any power factor
- 3
- Evaluate at x
- 1
Results
- (u/v)' = (u'v − uv')/v²
- 8.43492185
- u'v − uv'
- 2.46237790
- v²
- 0.29192658
- Value of u/v
- 1.85081572
Step by step
- 1Values used
- 2Quotient rule
- 3(u/v)' = (u'v − uv')/v²= 8.43492185
- 4u'v − uv'= 2.46237790
- 5v²= 0.29192658
- 6Value of u/v= 1.85081572
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Differentiate x³/cos x at x = 1.
(3x²cos x + x³ sin x)/cos²x = (3 cos 1 + sin 1)/cos²1 ≈ 8.4652.
Can I use the product rule instead?
Yes. Write u/v as u·v⁻¹ and apply the product and chain rules; you get the same answer.