Derivative Calculator

How to use this free online tool

This browser-based differentiation tool is built for calculus homework. Type a function of x (or change the variable), choose the derivative order from 1st to 5th, and press Calculate. You get a simplified result plus a rule-by-rule breakdown — power, product, quotient, and chain rules included.

Looking for a derivative solver, differentiation calculator, or dy/dx calculator? Same engine. Unlike Symbolab or Wolfram|Alpha Pro, step-by-step solutions stay free. No account. No upgrade prompt mid-homework.

How to find the derivative of a function

To find the derivative, identify which rule applies (power, product, quotient, or chain), differentiate, then simplify. The calculator automates that workflow and shows the working so you can learn — not just copy the final answer.

1. Enter the expression (use * for multiplication and ^ for powers).
2. Confirm the variable (usually x) and the order.
3. Read the labeled steps: which rule fired at each stage.
4. Compare the simplified derivative with your own work.

What functions this differentiation calculator supports

Polynomials and rational functions

Differentiate powers and fractions such as x^2, 3x, and 1/x with the power and quotient rules.

Trig and inverse trig

sin, cos, tan, sec, arcsin, arccos, arctan — including compositions via the chain rule.

Exponential and log

e^x, a^x, ln, and log10, with chain rule when the argument is itself a function.

Roots, absolute value, and higher-order derivatives

Roots and absolute value are supported. Raise the order to 2–5 for second (and higher) derivatives in the same workflow.

Common derivative examples (homework search patterns)

Students often search “derivative of …” for specific problems. Try these in the input above — they match frequent homework queries from organic search data:

Power-rule examples

• x — derivative of x is 1
• 3*x — derivative of 3x is 3
• x^2 / x^3 — power rule
• 1/x or x^(-1) — negative powers

Product, quotient, and chain examples

• x^2*sin(x) — product + chain
• (x^2+1)/(x-1) — quotient rule
• e^(3*x) — exponential chain rule
• ln(x^2+1) — log + chain
• (x+1)/(x-1) — classic rational example

Common derivative rules (quick reference)

Power rule

d/dx[xⁿ] = n·xⁿ⁻¹

Product rule

(fg)′ = f′g + fg′

Quotient rule

(f/g)′ = (f′g − fg′) / g²

Chain rule

(f(g(x)))′ = f′(g(x))·g′(x)

Sum and difference

Differentiate term by term.

Need the working spelled out for every rule? Open the derivative calculator with steps landing page — same free engine, steps-first framing.

Online tool vs paid solvers

Broad platforms often gate detailed steps behind a subscription. This site is a focused free differentiation / differential calculator for calculus homework: fast load, steps visible by default, and no login. Use it as a derivative finder to check answers, then study the labeled rules so you can reproduce them on paper.

Working with several variables? Switch to the partial derivative calculator to compute ∂f/∂x or ∂f/∂y while treating other letters as constants.

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