A simple polynomial
- Input
- d/dx (x^3 - 3x)
- Expected output
- 3x^2 - 3
Applies the power rule to each term and the difference rule to combine the two.
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derivative calculator
Searching for a "derivative calculator" often lands on tools that hide the step by step behind a subscription, giving away only the final answer for free. This page opens with a classic example (x³ - 3x, which shows the power and difference rules) and displays the full differentiation, no paywall.
Applies the power rule to each term and the difference rule to combine the two.
Chain rule: differentiate the sine on the outside and multiply by the derivative of x² on the inside.
Polynomials, trigonometric functions (sine, cosine, tangent and their inverses), hyperbolic functions, exponentials and logarithms, including combinations built from sums, subtraction, products, quotients and composition (the chain rule). Factorial, the remainder operator (%) and min/max are not elementarily differentiable, and the calculator says so instead of risking a wrong result.
It covers polynomials, trigonometric functions, hyperbolic functions, exponentials and logarithms, including combinations with sums, products, quotients and composition. Factorial, the remainder operator and min/max have no single elementary derivative, and the tool says so instead of risking a wrong answer.
Yes, the step by step is visible by default right below the result, with each rule named and the expression before and after it, and it can be collapsed with the "Show the step by step" switch if you only want the answer.
Examples by rule
3 * x^2 - 3
3 \cdot x^{2} - 3
No formula renderer on this page: copy the LaTeX above and paste it into an editor that displays it, like a document or a note.
Difference rule: the derivative of u - v is u' - v'.
Power rule (with the chain rule): the derivative of u^n, with n constant, is n * u^(n-1) * u'.
Derivative of the variable with respect to itself: the result is 1.
Product rule: the derivative of u * v is u' * v + u * v'.
Derivative of a constant: the result is always 0.
Derivative of the variable with respect to itself: the result is 1.
Everything runs in your browser: the expression you type, the symbolic differentiation and the graph never go through any server.