Calculus solver for derivatives & integrals
Apply the power rule step by step to find derivatives and integrals of 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.
What this calculus solver covers
This tool focuses on polynomial expressions in one variable — sums of terms like 4x^3 - 6x + 7, at any degree. It does not yet apply calculus rules (chain rule, product rule, etc.) to trigonometric, exponential, or logarithmic functions, and it doesn't cover multivariable calculus. SolveStep's arithmetic mode can numerically evaluate sin, cos, tan, log, and ln for a specific number, which is useful for checking a value, but that's separate from differentiating or integrating them symbolically.
How do I write a derivative?
Use d/dx(3x^2 + 2x), or plain English like derivative of 3x^2 + 2x.
How do I write an integral?
Use integrate 3x^2 + 2x. The result always includes "+ C" for the constant of integration.
Does it differentiate trig or logarithmic functions?
Not yet — the derivative and integral engine covers polynomial terms only. SolveStep can numerically evaluate sin, cos, tan, log, and ln for a specific angle or number, but it doesn't yet apply calculus rules like the chain rule to them.
What polynomial degree can it handle?
Any degree — the power rule is applied term by term regardless of how many terms or how high the exponents are, as long as exponents are non-negative whole numbers.
Is there a calculus math solver that's actually free?
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.