Derivative & Integral Calculator
Calculate derivatives and integrals with step-by-step solutions
Calculus Operations
How to Use the Calculus Calculator
Function Notation
- Powers: Use ^ for exponents (e.g., x^2, x^3)
- Multiplication: Use * or simply write 3x for 3*x
- Constants: Numbers without variables (e.g., 5, -2, 3.14)
- Variables: Single letters (x, y, t, etc.)
Derivative Rules
- Power Rule: d/dx[x^n] = nx^(n-1)
- Constant Rule: d/dx[c] = 0
- Sum Rule: d/dx[f + g] = f' + g'
- Product Rule: d/dx[fg] = f'g + fg'
- Chain Rule: d/dx[f(g(x))] = f'(g(x)) × g'(x)
Integration Rules
- Power Rule: ∫x^n dx = x^(n+1)/(n+1) + C
- Constant Rule: ∫c dx = cx + C
- Sum Rule: ∫(f + g) dx = ∫f dx + ∫g dx
- Fundamental Theorem: ∫[a to b] f(x) dx = F(b) - F(a)
Educational Applications
- Calculus Homework: Step-by-step solutions for learning
- Rate of Change: Find instantaneous rates using derivatives
- Area Under Curves: Calculate areas using definite integrals
- Optimization: Find maxima and minima using calculus
Frequently Asked Questions
What functions can this calculator handle?
This calculator can handle basic polynomial functions, simple trigonometric functions, and exponential functions. For complex functions involving logarithms, inverse trig functions, or complex compositions, use specialized computer algebra systems.
What is the difference between indefinite and definite integrals?
Indefinite integrals (antiderivatives) include a constant of integration (+C) and represent a family of functions. Definite integrals evaluate to a specific number representing the area under the curve between two limits.
How do I interpret the constant of integration?
The constant C in indefinite integrals represents any constant value, since the derivative of a constant is zero. When solving initial value problems, this constant is determined by boundary conditions.
Can I check if my manual calculations are correct?
Yes! Use this calculator to verify your derivatives and integrals. The step-by-step solutions help you understand where errors might occur in manual calculations.
Related Calculators
- Limit Calculator - For calculating limits and continuity
- Algebra Solver - For solving polynomial equations
- Graphing Calculator - To visualize functions and their derivatives
- Complex Number Calculator - For calculus with complex functions