Derivative Calculator

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Simple Derivative Calculator

Advanced Derivative Calculator with Graph

Online Derivative Calculator – Instant Differentiation with Graph

Welcome to the free online Derivative Calculator – a powerful and easy-to-use tool that helps you compute the derivative of any mathematical function in seconds.

  • Differentiate functions with respect to any variable (x, y, t, etc.)
  • Get simplified output instantly
  • Visualize original and derivative graphs (advanced)
  • Use trigonometric, exponential, logarithmic, rational, and polynomial expressions

What is a Derivative?

A derivative represents the rate of change or slope of a function. In simple terms, it tells you how fast something is changing at any point.

Derivative Formula

If \( f(x) \) is a function, then the derivative of \( f \) with respect to \( x \) is:

\( f'(x) = \frac{d}{dx}f(x) \)

Common Derivative Rules

Rule Formula
Power Rule\( \frac{d}{dx}x^n = nx^{n-1} \)
Constant Rule\( \frac{d}{dx}c = 0 \)
Sum Rule\( \frac{d}{dx}(f + g) = f’ + g’ \)
Product Rule\( \frac{d}{dx}(fg) = f’g + fg’ \)
Quotient Rule\( \frac{d}{dx}\left(\frac{f}{g}\right) = \frac{f’g – fg’}{g^2} \)
Chain Rule\( \frac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x) \)
Trigonometric\( \frac{d}{dx}\sin(x) = \cos(x), \quad \frac{d}{dx}\tan(x) = \sec^2(x) \)

Examples

  • \( \frac{d}{dx}(x^2 + 3x) = 2x + 3 \)
  • \( \frac{d}{dx}(\sin(x)) = \cos(x) \)
  • \( \frac{d}{dx}(e^x) = e^x \)
  • \( \frac{d}{dx}(\ln(x)) = \frac{1}{x} \)

Features of This Calculator

FeatureSimple VersionAdvanced Version
Supports polynomials, sin, cos, log, exp✔️✔️
Custom variable (x, y, t…)✔️✔️
Step-by-step output✔️✔️
Graph plotting✔️
LaTeX Math Output✔️
Mobile friendly✔️✔️

Use Cases

  • ✅ For class 11/12 students studying calculus
  • ✅ For engineering and science students
  • ✅ For quick homework checks
  • ✅ For plotting and visualizing changes

How It Works

  1. Enter the function like x^3 + 2x
  2. Specify the variable (default is x)
  3. Hit “Calculate”
  4. View the simplified derivative
  5. (Advanced only) View the graph of f(x) and f'(x)

Supported Functions

  • Algebra: x^2, 3*x + 2, (x + 1)^3
  • Trigonometry: sin(x), cos(x), tan(x)
  • Exponential: e^x, 2^x
  • Logarithms: ln(x), log10(x)
  • Combinations: x^2 * sin(x), ln(x^2 + 1)