Calculus solver for derivatives & integrals
Find derivatives step by step, with the chain, product and quotient rules included alongside sin, cos, tan, eˣ and log, and integrate polynomial expressions of any degree.
Part of SolveStep's free math solver, alongside dedicated tools for algebra, geometry, statistics, and matrices.
The power rule, term by term
For each term c·xⁿ, the derivative is c·n·x^(n-1). Type d/dx(...), "derivative of ...", or "differentiate ..." followed by your expression, and SolveStep will apply the rule to every term and combine the results.
Reverse power rule with +C
For each term c·xⁿ, the antiderivative is c/(n+1)·x^(n+1). Type "integrate ..." followed by your expression to see each term integrated individually, plus the constant of integration.
The power rule, applied term by term
Derivative of a cubic
d/dx(x³ − 4x + 7)- Apply the power rule to x³: multiply by the exponent 3, then reduce it by 1 → 3x².
- Apply it to -4x: multiply -4 by exponent 1, reduce the exponent to 0 → -4.
- The constant 7 has a derivative of 0, since a flat number never changes.
- Combine the surviving terms.
The chain rule, step by step
Derivative of a composed sine
d/dx(sin(3x + 1))- The outside function is sin(u), where u = 3x + 1. The derivative of sin(u) is cos(u).
- Differentiate the inside: u' = d/dx(3x + 1) = 3.
- Chain rule: multiply the outside derivative by the inside derivative.
What this calculus solver covers
Derivatives: any expression built from polynomials, sin, cos, tan, eˣ, aˣ, ln, log, sqrt, cbrt, and the inverse trig functions (asin/acos/atan), combined with sums, products, quotients and composition. The chain, product and quotient rules are all applied automatically, and each rule appears as its own step. Trig arguments are treated in radians here, the standard convention for calculus (SolveStep's arithmetic-mode sin()/cos()/tan() stay in degrees, since that's a separate, simpler use of the same function names). Integrals are still polynomial-only for now, so integrate sin(x) and its relatives are not supported yet, even though the derivative side handles them. Logarithmic differentiation (both the base and the exponent containing x, like x^x) and multivariable calculus aren't covered.
How do I write a derivative?
Use d/dx(3x^2 + 2x), or plain English like derivative of 3x^2 + 2x. Composed expressions work the same way: d/dx(sin(3x + 1)) or d/dx(e^(2x)).
How do I write an integral?
Use integrate 3x^2 + 2x. The result always includes "+ C" for the constant of integration. Integration currently covers polynomials only.
Does it differentiate trig, exponential, or logarithmic functions?
Yes. The derivative engine knows the derivatives of sin, cos, tan, eˣ, aˣ, ln, log, sqrt, cbrt and inverse trig, and it handles compositions such as sin(3x + 1) or e^(2x) through the chain rule.
Does it handle the chain rule?
Yes. Any composed expression is differentiated by combining the outer function's derivative with the inner expression's derivative automatically, and the step-by-step breakdown names the rule (chain, product, or quotient) as it's applied.
What polynomial degree can it handle?
Any degree. The power rule is applied term by term no matter how many terms there are or how high the exponents go, as long as those exponents are non-negative whole numbers.
Is there a calculus math solver that is free with steps?
Yes. This one. There's no paywall, account, or limit on how many derivatives or integrals you can solve, and nothing you type is sent to a server.