Free Calculus Solver — derivatives & integrals

Free Calculus Solver
with Step-by-Step AI

Derivatives, integrals, limits and optimization — complete worked solution with every rule identified and explained. No paywall.

  • Derivatives & differentiation rules
  • Definite & indefinite integrals
  • Limits & L’Hôpital’s rule
  • Optimization problems
← Back to all math tools
Calculus Solver — MathGPT Free ✓ Free
Ctrl+Enter to solve
Parsing problem…

Step 2: f'(x)=3x²·sin(x)+x³·cos(x)

Simplified: f'(x)=x²(3sin(x)+x·cos(x))

Final: f'(x)=x²(3sin(x)+x·cos(x))

View Full Solution →
✓Derivatives & differentiation rules
✓Definite & indefinite integrals
✓Limits & L’Hôpital’s rule
✓Optimization problems
Calculus Solver — MathGPT Free — More Examples
✓ Step-by-step · Free
f(x)=x³·sin(x)∫(x²+4x−1)dx, 0 to 3lim sin(x)/x as x→0Chain rule: (3x²+1)⁵
Insert:

Ctrl+Enter to solve instantly

Subject: Calculus
Parsing your calculus problem…
Identifying the solution method
Working through each step
Verifying the final answer
Solution Ready

Step 2: f'(x)=3x²·sin(x)+x³·cos(x)

Simplified: f'(x)=x²(3sin(x)+x·cos(x))

Final: f'(x)=x²(3sin(x)+x·cos(x))

Full step-by-step solution is ready

View Full Solution →
How It Works

From problem to solution in seconds

01

Enter your calculus problem

Type any derivative, integral, or limit. Use ∫ and ∂ buttons or type ‘integral’, ‘d/dx’ in plain text.

02

AI identifies the calculus rule

Detects chain, product, quotient rule, integration by parts, substitution, or L’Hôpital and applies it correctly.

03

Follow each step in plain language

See which rule was applied and why at each stage — not just a symbolic transformation.

Topics Covered

What this calculus solver handles

d/dx
Differentiation
Power, chain, product, quotient rules, implicit differentiation.
∫
Integration
Indefinite/definite integrals, substitution, integration by parts.
→
Limits
One-sided limits, L’Hôpital’s rule, limits at infinity.
📈
Optimization
Maxima/minima with first and second derivative tests.
📐
Related Rates
Implicit differentiation applied to real-world problems.
∑
Series
Taylor, Maclaurin series, convergence tests.

What Is a Free Calculus Solver?

A calculus solver takes a differentiation, integration, or limit problem and returns a complete worked solution. MathGPT Free uses AI to identify which rule applies — chain rule, product rule, integration by parts, L’Hôpital — and explains each step in conversational language.

It covers Calculus I and II: derivatives of algebraic and trigonometric functions, definite and indefinite integrals, limits, and optimization. The step-by-step format helps build understanding rather than just providing a number.

Solving Derivatives, Integrals, and Limits

Derivatives

Applies power rule (xⁿ→nxⁿ⁻¹), product rule, quotient rule, chain rule for composite functions. Implicit and logarithmic differentiation also supported.

Integrals

Power rule in reverse, trigonometric integrals, substitution, integration by parts. For definite integrals, evaluates at bounds and subtracts.

Limits

Standard limits, one-sided limits, limits at infinity, indeterminate forms using L’Hôpital’s rule — each algebraic step shown.

Calculus Problems This Solver Handles

  • Derivatives of polynomial, trig, exponential, logarithmic functions
  • Chain rule, product rule, quotient rule problems
  • Implicit differentiation
  • Indefinite and definite integrals
  • Substitution and integration by parts
  • Limits including L’Hôpital’s rule
  • Optimization: maxima and minima
  • Related rate problems
What Students Say

Real results from real students

★★★★★

“I failed to understand integration by parts after reading the textbook three times. This explained it in two paragraphs I actually got.”

Rania K.
Calc II student
★★★★★

“Tried Symbolab — it gave me the formula. This walks through why we use the chain rule here.”

Tom B.
Engineering undergrad
★★★★☆

“Good for checking my work and seeing if I applied the correct rule. Saves time on long problem sets.”

Mei L.
Math major, sophomore
FAQ

Common questions

Yes. The solver identifies the rule before applying it and explains why that rule fits the function structure.
Yes. Enter bounds like ‘from 0 to 3’. The solver evaluates the antiderivative at each bound and subtracts.
Yes — sin, cos, tan and their inverses are supported for both differentiation and integration.
Yes. For 0/0 or ∞/∞ forms, it applies L’Hôpital and shows each differentiation step.
Wolfram Alpha requires Pro for detailed steps. MathGPT Free gives full steps at no cost, in plain language.
Related Tools

More free math solvers

Algebra SolverEquations, systems, polynomialsGeometry SolverArea, volume, trianglesTrigonometry SolverSin, cos, tan, identities

Ready to solve your calculus problem?

Full derivatives, integrals, and limits — free, no signup.

Get the Full Solution →