How is the numerical derivative calculated?

Using the central finite difference quotient: f’(x0) ≈ [f(x0 + h) - f(x0 - h)] / (2h), with step size h = 10⁻⁵ for high numerical stability and O(h²) accuracy.

How is the definite integral computed?

The integral is computed using Composite Simpson’s 1/3 Rule partitioned into 1,000 subintervals, providing fourth-order numerical precision for continuous functions.

Calculators & Converters•Free Online Tool

Calculus, Derivatives & Definite Integrals Calculator

Professional calculus computation tool. Computes numerical first and second derivatives at any point x0 via central difference quotients, formulates tangent line equations y = mx + b, and calculates definite integrals ∫[a,b] f(x) dx using Composite Simpson’s 1/3 Rule across 1,000 subintervals.

100% Free & Private

Calculus & Derivatives Calculator

Compute numerical derivatives (f', f''), tangent line equations, and definite integrals (Simpson's rule) with high precision.

Function & Parameters

Select Target Function

f(x) = x³ - 3x² + 2

Evaluation Point (x₀)

Derivative Results

First Derivative f'(2)

0.0000

Instantaneous rate of change / slope at x = 2

Function Value f(2)

-2.0000

Second Derivative f''(2)

6.0000

Tangent Line Equation:

y = 0.0000x - 2.0000

Calculus Formulas & Methodology

Difference Quotient: f'(x₀) ≈ [f(x₀ + h) - f(x₀ - h)] / 2h

Second Derivative: f''(x₀) ≈ [f(x₀ + h) - 2f(x₀) + f(x₀ - h)] / h²

Tangent Line: y - f(x₀) = f'(x₀)(x - x₀)

How to Use Calculus, Derivatives & Definite Integrals Calculator

Choose Mode

Select Derivative & Tangent Line or Definite Integral.

Select Function & Coordinates

Pick a mathematical function and set evaluation point x0 or integration bounds [a, b].

View Slope & Tangent Equation

Review the derivative, curvature (f’’), tangent equation, or net signed area.

Frequently Asked Questions

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Calculators & Converters•Free Online Tool

Calculus, Derivatives & Definite Integrals Calculator

100% Free & Private

Calculus & Derivatives Calculator

Compute numerical derivatives (f', f''), tangent line equations, and definite integrals (Simpson's rule) with high precision.

Function & Parameters

Select Target Function

f(x) = x³ - 3x² + 2

Evaluation Point (x₀)

Derivative Results

First Derivative f'(2)

0.0000

Instantaneous rate of change / slope at x = 2

Function Value f(2)

-2.0000

Second Derivative f''(2)

6.0000

Tangent Line Equation:

y = 0.0000x - 2.0000

Calculus Formulas & Methodology

Difference Quotient: f'(x₀) ≈ [f(x₀ + h) - f(x₀ - h)] / 2h

Second Derivative: f''(x₀) ≈ [f(x₀ + h) - 2f(x₀) + f(x₀ - h)] / h²

Tangent Line: y - f(x₀) = f'(x₀)(x - x₀)

How to Use Calculus, Derivatives & Definite Integrals Calculator

Choose Mode

Select Derivative & Tangent Line or Definite Integral.

Select Function & Coordinates

Pick a mathematical function and set evaluation point x0 or integration bounds [a, b].

View Slope & Tangent Equation

Review the derivative, curvature (f’’), tangent equation, or net signed area.

Frequently Asked Questions

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Full mathematical expression evaluator supporting brackets, powers, scientific notation, and calculation audit log.

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Full Scientific Calculator (Trig, Log & Rad/Deg)

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Open Tool

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Find global maximum and minimum values of functions on closed intervals [a, b] using the Extreme Value Theorem.

Open Tool

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Calculate percentages, percentage increases, decreases, and percentage differences.

Open Tool