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Basic Calculus Calculator
Derivatives
Integrals
Limits
Derivative Calculator (Polynomials)
Enter Function f(x)
f(x) = x³ + 2x² - 5x + 1
Find Derivative
Example Functions
x²
3x³ - 2x
x⁴ + x³ - x² + x
5x² + 3x - 7
Derivative Rules
d/dx(x^n) = n*x^(n-1) (Power Rule)
d/dx(c*f(x)) = c*f'(x) (Constant Multiple)
d/dx(f(x) + g(x)) = f'(x) + g'(x) (Sum Rule)
d/dx(c) = 0 (Constant Rule)
Integral Calculator (Basic Indefinite)
Enter Function f(x)
∫(2x + 3)dx
Find Integral
Example Functions
x
x²
3x² + 2x
x³ - 4x + 5
Integration Rules
∫x^n dx = x^(n+1)/(n+1) + C (Power Rule)
∫c*f(x) dx = c*∫f(x) dx (Constant Multiple)
∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx (Sum Rule)
∫c dx = c*x + C (Constant Rule)
Limit Calculator (Basic)
Enter Function f(x)
x approaches
Direction
Both sides
From left (x→a⁻)
From right (x→a⁺)
lim(x→1) (x²-1)/(x-1)
Find Limit
Example Limits
x² as x→2
(x²-4)/(x-2) as x→2
(x²-1)/(x-1) as x→1
1/x as x→0
Limit Techniques
Direct substitution (if no 0/0 form)
Factoring and canceling
L'Hôpital's rule (for 0/0 or ∞/∞)
Numerical approximation