Free Derivative Calculator with Steps

Calculate derivatives instantly with step-by-step solutions, interactive graphs, 3D visualization, and comprehensive analysis

✅ 100% Free Forever ⚡ Advanced Features 📊 Interactive Graphs 📱 Mobile Optimized
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📊 Step-by-Step Solutions
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🧮 Advanced Derivative Calculator

Differentiate w.r.t: Order:

📊 Calculation Options

📚 Quick Examples

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Calculating derivative...

📈 Analysis Results

📝 Original Function
⚡ Derivative Result
📊 Numerical Value
Enter evaluation point

📈 Function Visualization

📋 Derivative Properties

Property Value Description

🔬 Step-by-Step Solution

📚 Calculation History

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🎯 Practice Problem
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Advanced Calculations

Calculate up to 5th-order derivatives, evaluate at specific points, and get comprehensive function analysis with our enhanced algorithms.

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Interactive Visualization

Visualize functions and derivatives with interactive 2D/3D graphs. Zoom, pan, and explore mathematical relationships in real-time.

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Mobile Optimized

Works perfectly on all devices - smartphones, tablets, laptops, and desktops. Touch-optimized controls for mobile users.

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100% Free & Advanced

No sign-up required. No hidden fees. All advanced features are completely free forever with unlimited calculations.

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Comprehensive Analysis

Get detailed function properties, critical points, asymptotes, and complete derivative tables with step-by-step explanations.

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Privacy First

Your calculations are private and secure. We don't store your data or track your activity. Complete anonymity guaranteed.

📖 Advanced Derivative Calculator

Our advanced derivative calculator represents the next generation of mathematical computation tools. Unlike basic calculators, it provides comprehensive analysis including interactive 2D/3D graphing, higher-order derivatives (up to 5th order), numerical evaluation at specific points, and detailed function properties.

The calculator uses professional-grade algorithms to compute derivatives instantly while providing educational insights. It automatically detects function types (polynomial, trigonometric, exponential, logarithmic), identifies critical points, determines concavity, and provides comprehensive analysis that helps students understand not just the "what" but the "why" behind derivatives. If you are working on complex problems like chain rule or product rule, this tool simplifies the process.

Key advanced features include: Real-time LaTeX preview of your input, interactive graphing with tangent lines, 3D visualization for multivariable concepts, calculation history with localStorage persistence, and export capabilities for graphs and results. The interface is designed for both beginners and advanced users, with quick access tools and comprehensive options.

🎯 How to Use Advanced Features

Maximize your learning with these advanced features:

Advanced Feature Guide

  1. Higher-Order Derivatives: Use the order selector to calculate 2nd, 3rd, 4th, or 5th derivatives. Perfect for studying concavity and higher-order behavior.
  2. Interactive Graphs: Click and drag to explore functions. Use zoom controls to examine details. Toggle between function and derivative views.
  3. 3D Visualization: Explore multivariable concepts with our 3D graph feature. Rotate, zoom, and examine surfaces from different angles.
  4. Numerical Evaluation: Enter a specific x-value in the evaluation point field to get the exact derivative value at that point.
  5. Calculation History: Access your previous calculations via the history panel. Perfect for reviewing problems or continuing work.
  6. Export Tools: Save graphs as PNG images or export complete results as PDF reports for study or submission.

Pro Tips: Use the math toolbar for quick symbol insertion. Enable LaTeX preview for better equation visualization. Save complex calculations to history for quick reference. The calculator supports all standard mathematical functions including trigonometric (sin, cos, tan), exponential (e^x), logarithmic (ln, log), hyperbolic functions, and custom combinations.

📐 Advanced Derivative Formulas

Our advanced calculator handles these complex differentiation formulas automatically:

Higher-Order Rules

  • 2nd Derivative: f''(x) = d²/dx²[f(x)]
  • Leibniz Notation: dⁿ/dxⁿ[f(x)·g(x)]
  • General Power: dⁿ/dxⁿ[xᵐ] = m!/(m-n)!·xᵐ⁻ⁿ
  • Trig Higher: dⁿ/dxⁿ[sin(x)] = sin(x + nπ/2)

Advanced Rules

  • Implicit: d/dx[f(y)] = f'(y)·dy/dx
  • Parametric: dy/dx = (dy/dt)/(dx/dt)
  • Inverse: d/dx[f⁻¹(x)] = 1/f'(f⁻¹(x))
  • Logarithmic Diff: d/dx[y] = y·d/dx[ln(y)]

Special Functions

  • Hyperbolic: d/dx[sinh(x)] = cosh(x)
  • Inverse Trig: d/dx[arcsin(x)] = 1/√(1-x²)
  • Gamma: d/dx[Γ(x)] = Γ(x)·ψ(x)
  • Bessel: d/dx[Jₙ(x)] = ½[Jₙ₋₁(x)-Jₙ₊₁(x)]

New to Derivatives?

Start with our Interactive Derivative Rules Hub to learn the fundamentals with 50+ examples and practice problems.

⭐ Why Choose Our Advanced Calculator?

Comparison of advanced features across popular derivative calculators:

Advanced Feature Our Calculator Symbolab WolframAlpha
3D Visualization
Interactive Graphing Limited Static
5th Order Derivatives
Calculation History
Export Graphs
Mobile Touch Optimized
All Features Free

❓ Advanced Features FAQ

What makes this calculator "advanced"?

Our advanced calculator includes features not found in basic tools: interactive 2D/3D graphing, higher-order derivatives (up to 5th), numerical evaluation at points, calculation history with localStorage, export capabilities, touch-optimized mobile interface, and comprehensive function analysis with properties tables.

Can I calculate higher-order derivatives?

Yes! Use the order selector to calculate 2nd, 3rd, 4th, or 5th derivatives. This is perfect for studying concavity (2nd derivative), jerk (3rd derivative), and higher-order behavior in physics and engineering applications.

How does 3D visualization work?

The 3D visualization creates interactive surface plots for functions of two variables. You can rotate, zoom, and explore mathematical surfaces from any angle. This is particularly useful for multivariable calculus and visualizing partial derivatives.

Is my calculation history saved?

Yes! All calculations are saved in your browser's localStorage. You can access them anytime via the history panel. This allows you to review previous work, continue calculations, or create study references. Your history remains private and is only accessible from your device.

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📚 Advanced Learning Resources

Master calculus with our comprehensive collection of free learning resources. From beginner guides to advanced techniques, we provide everything you need to excel in derivatives and calculus.

✨ Featured Resource

Derivative Rules Cheat Sheet

Download our comprehensive cheat sheet covering all derivative rules including power rule, product rule, quotient rule, chain rule, trigonometric, exponential, and logarithmic derivatives.

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Updated: Dec 2025
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