Derivative Calculator

This calculator is designed to help students and professionals compute derivatives of functions easily. By entering a function and specifying the variable, users can see immediate results, helping in understanding calculus concepts or solving mathematical problems.

Interactive Calculator

Results

Derivative:
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Data Source and Methodology

All calculations are strictly based on standard mathematical formulas for derivatives. For further mathematical rigor, please refer to calculus textbooks and scholarly articles.

The Formula Explained

Power Rule: \( \frac{d}{dx} x^n = n \cdot x^{n-1} \)

Product Rule: \( \frac{d}{dx} (uv) = u'v + uv' \)

Chain Rule: \( \frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x) \)

Glossary of Variables

Practical Example: Step-by-Step

Consider the function \( f(x) = x^2 + 3x + 2 \). To find the derivative, apply the power rule to get \( f'(x) = 2x + 3 \).

Frequently Asked Questions (FAQ)

What is a derivative?

A derivative represents the rate of change of a function with respect to a variable.

How do I calculate a derivative?

You can calculate a derivative by using rules of differentiation, such as the power rule, product rule, and chain rule.

Why are derivatives important?

Derivatives are fundamental in calculus for understanding changes, modeling real-world situations, and solving problems in science and engineering.

Can the calculator handle complex functions?

Our calculator is designed to handle a wide range of functions, but for highly complex expressions, manual verification is recommended.

What is the chain rule?

The chain rule is a formula for computing the derivative of the composition of two or more functions.

Tool developed by Ugo Candido. Content reviewed by the CalcDomain Expert Team. Last revised for accuracy on: October 15, 2023.

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