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Derivative Calculator with steps

Enter a function, choose the order and the variable, and see the derivative with the differentiation rule behind every term.

Try:

Answer

Enter your numbers or pick an example — the answer and the steps appear here instantly.

What you get back

  • The rule for each term

    Sum, constant, constant multiple, power, product, quotient, chain and exponential rules are named where they apply, plus logarithmic differentiation for forms like x^x.

  • Up to the third derivative

    Pick first, second or third order. Each higher order comes from differentiating the previous result once more.

  • Value at a point

    Give an x-value to evaluate the derivative there, exact when possible plus a decimal. That number is the slope of the tangent line at the point.

  • Numerically checked

    Before the result appears, it is compared with a numerical derivative of your function, which catches algebra slips.

  • Tidy polynomial output

    Polynomial answers are written in descending powers, the form most answer keys use.

  • Any variable

    Differentiate with respect to x, t or whichever single letter your function is written in.

How to find a derivative by hand

These rules cover the functions you meet in a first calculus course.

  • Power rule

    d/dx xⁿ = n·xⁿ⁻¹. So d/dx x⁵ = 5x⁴, and since √x = x^(1/2), its derivative is (1/2)x^(−1/2) = 1/(2√x).

  • Product rule

    (uv)′ = u′v + uv′. For x²·sin x, take u = x² and v = sin x to get 2x·sin x + x²·cos x.

  • Quotient rule

    (u/v)′ = (u′v − uv′)/v². For x/(x + 1) that is ((x + 1) − x)/(x + 1)², which simplifies to 1/(x + 1)².

  • Chain rule

    Differentiate the outer function, leave the inside alone, then multiply by the derivative of the inside: d/dx sin(3x²) = cos(3x²)·6x.

  • Exponentials and logarithms

    d/dx eˣ = eˣ, d/dx aˣ = aˣ·ln a and d/dx ln x = 1/x. Combined with the chain rule, d/dx e^(2x) = 2e^(2x).

  • Logarithmic differentiation

    For y = x^x, take ln of both sides: ln y = x·ln x. Differentiating gives y′/y = ln x + 1, so y′ = x^x(ln x + 1).

Using the derivative calculator

  1. Enter the function

    Type it with ^ for powers and * for products, e.g. x^2 * sin(x) or e^(2x)/x.

  2. Set order, variable and point

    Choose first, second or third derivative. The evaluation point is optional.

  3. Calculate

    Read the derivative, the rule used for each term and, if you gave a point, the exact and decimal value there.

  4. Get a written explanation

    Select “Explain step by step” for the AI Math Solver's full reasoning, then continue in AI Chat if a step still feels unclear.

Frequently asked questions

It measures how the slope itself is changing. A positive second derivative means the graph is concave up there and a negative one means concave down; where it changes sign you may have an inflection point.

Derivatives can be written in many equivalent forms: 2x·sin x + x²·cos x and x(2 sin x + x cos x) are the same function. Evaluate both at the same point to confirm they agree.

Yes. Type the value in the optional box and you get the derivative at that point, exactly when possible, along with a decimal. A decimal that had to be rounded is shown with ≈.

Yes. Results and rule outlines are computed in your browser by our own code, free and without an account. For a full written walkthrough, the AI explanation is included in the Pro plans* (*fair use: up to 300 runs a day across the writing, study and code tools) or costs 2 credits without a plan; signed-out visitors can preview how it begins.

It can. The calculator's own result is checked against a numerical derivative before display, but the AI-written reasoning is not, so read it critically. Use both for study and self-checking, and follow your course's rules on AI help.

The calculator takes typed input only. If all you have is a photo, the AI Math Solver accepts images and can work from there.

More calculus tools

Differentiate with the rules in view

Enter a function and see which rule handles each term, verified against a numerical derivative.

Find a derivative
  • Power, product, quotient and chain rules
  • First to third order
  • Exact value at a point