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Partial Derivative Calculator

Compute partial and mixed derivatives of a multivariable function symbolically.

Related tools

All Calculus tools →
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Open Partial Derivative Calculator and you get an answer straight away, with no account to create. It sits under Calculus in our catalogue, alongside Partial Fraction Decomposition Calculator and Derivative Calculator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Partial Derivative Calculator?

Compute partial and mixed derivatives of a multivariable function symbolically.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Partial Derivative Calculator different from Partial Fraction Decomposition Calculator?

They sit next to each other but answer different questions: Partial Fraction Decomposition Calculator is the one to open when you need it to breaks a rational function into simple fractions, covering distinct linear factors, repeated factors and irreducible quadratics. The setup and the linear system solved for the coefficients are both shown, since that is the part being learned. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Derivative Calculator is the closest one after this: Compute single, partial, implicit and directional derivatives symbolically.

What else is worth having open alongside it?

Directional Derivative Calculator and Implicit Derivative Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.