Derivative Calculator

Free derivative calculator with steps: differentiate any function using the power, product, quotient and chain rules, get higher-order, partial and implicit derivatives, evaluate at a point and plot f and f′.

d/dx
Press Enter to run. Steps, a plot and a check against SymPy come with every answer.

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Free online derivative calculator with steps

Type a function the way you would write it on paper — x^2 sin x, 2x, e^(3x), sqrt x, ln(cos x), |x|, sin^2 x or with Greek letters such as θ and α — and get its derivative with a full step-by-step solution. Every step names the rule it uses (constant, power, sum, product, quotient, chain rule with the inner and outer function, exponential and logarithm rules, trigonometric, inverse trigonometric and hyperbolic derivatives, absolute value and logarithmic differentiation for functions like x^x), shows the rule, the substitution and the result, and finishes with a simplification.

  • Higher derivatives up to the 5th, each order with its own steps.
  • Partial derivatives: pick the variable (y), or list several (x, y) for a mixed partial derivative.
  • Implicit differentiation: type an equation such as x^2 + y^2 = 25 to get dy/dx.
  • Evaluate at a point and get the tangent line there.
  • A plot of f and f′, a link to open both in the 2D graphing calculator, and a check of the answer against SymPy.

How it works

The maths runs in your own browser: the first time you press Differentiate, the page downloads SymPy, the open-source computer algebra system, together with a WebAssembly build of Python (about 10 MB, cached by your browser afterwards). Nothing you type is sent to a server. The step-by-step explanation comes from MES's own rule-based differentiator, and the final answer is checked against SymPy's.

Tips

Multiplication
Write 2x, x sin x or use *, · or ×. xy means x times y.
Functions
ln and log are the natural logarithm; log_2(x) or log10(x) for other bases. sin^2 x is (sin x)², sin^-1 x is arcsin x.
Constants
e, pi or π; every other letter is a variable.
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