Derivative Calculator with Steps
Type a function and get its derivative worked out the way a calculus teacher writes it: the sum rule splits it into terms, constant factors come out front, the product and quotient rules name u and v and their derivatives, and the chain rule separates the outside from the inside before multiplying. Covers powers and roots, eˣ and aˣ, ln and log, all six trigonometric functions, arcsin, arccos, arctan and the hyperbolic functions, absolute values, and logarithmic differentiation for functions like xˣ. Ask for the second, third or fourth derivative, or give a point to get the slope and the tangent line there; a graph shows the function next to its derivative.
Read the full guide to this tool
Results
Notes
- The core rules: (u + v)′ = u′ + v′, (cu)′ = cu′, (xⁿ)′ = nxⁿ⁻¹, (uv)′ = u′v + uv′, (u/v)′ = (u′v − uv′)/v² and the chain rule (f(g(x)))′ = f′(g(x))·g′(x).
- Answers are shown the way the rules produce them and then simplified; textbook answers can look different but be equal — expand or factor to compare.
- Every result is checked against a computer algebra system, so a wrong step is never reported as the answer.
- Angles are in radians: the rule (sin x)′ = cos x only holds when x is measured in radians.
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