Calculus Calculator
Calculate derivatives, integrals, limits, and solve calculus problems step-by-step
Use: x^2, sqrt(x), sin(x), cos(x), tan(x), ln(x), e^x, pi
For limits at 0, try using a small value like 0.0001
Derivative at x = Definite Integral from to Limit as x →
f() ∫ f(x) dx limx→ f(x)
Calculation Details
Derivatives
d/dx(xⁿ) = n·xⁿ⁻¹
d/dx(sin x) = cos x
d/dx(cos x) = -sin x
d/dx(eˣ) = eˣ
d/dx(ln x) = 1/x
Integrals
∫xⁿ dx = xⁿ⁺¹/(n+1) + C
∫sin x dx = -cos x + C
∫cos x dx = sin x + C
∫eˣ dx = eˣ + C
∫1/x dx = ln|x| + C
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About Calculus Calculator
What is a Calculus Calculator?
A calculus calculator is a powerful mathematical tool that helps you solve calculus problems including derivatives, integrals, limits, and series. Our calculator provides step-by-step solutions to help you understand the solving process.
How to Use This Calculator
- Select Operation: Choose the type of calculus operation (derivative, integral, limit, or series)
- Enter Function: Type your mathematical function using standard notation
- Set Parameters: Specify the variable, limits, or bounds as needed
- Calculate: Click calculate to get your result with steps
Available Operations
Derivatives
Find the rate of change of a function with respect to a variable. Supports:
- First-order derivatives (f'(x))
- Higher-order derivatives (f''(x), f'''(x))
- Partial derivatives
Definite Integrals
Calculate the area under a curve between two bounds. Enter:
- The function to integrate
- Lower and upper bounds
- The variable of integration
Limits
Evaluate what value a function approaches as the input approaches a specific value:
- One-sided limits (left and right)
- Limits at infinity
- L'Hôpital's rule applications
Series Expansions
Expand functions as infinite series:
- Taylor series
- Maclaurin series
- Power series
Common Functions Notation
| Function | How to Type |
|---|---|
| x squared | x^2 or x**2 |
| Square root | sqrt(x) |
| Natural log | ln(x) |
| Exponential | e^x or exp(x) |
| Sine | sin(x) |
| Cosine | cos(x) |
| Tangent | tan(x) |
| Pi | pi |
Frequently Asked Questions
What is a derivative?
A derivative measures the instantaneous rate of change of a function. It represents the slope of the tangent line to the function's graph at any point.
What is an integral?
An integral calculates the accumulated area under a curve. Definite integrals give a numerical value, while indefinite integrals give a function family.
What is a limit?
A limit describes the value that a function approaches as the input approaches a specified value. Limits are fundamental to defining derivatives and integrals.
How accurate are the calculations?
Our calculator uses numerical methods that provide high accuracy for most functions. Complex expressions may have small rounding errors.
Fundamental Theorems
Fundamental Theorem of Calculus
The derivative and integral are inverse operations:
- d/dx ∫f(t)dt = f(x)
- ∫f'(x)dx = f(x) + C
Power Rule
- Derivative: d/dx(x^n) = n·x^(n-1)
- Integral: ∫x^n dx = x^(n+1)/(n+1) + C
Note: This calculator provides numerical approximations and symbolic solutions for common functions. For complex mathematical proofs or advanced analysis, consult a mathematics professional.