Master calculus with our comprehensive collection of 15+ free derivative calculators. Each tool provides step-by-step solutions, detailed explanations, and interactive features to help you understand differentiation concepts including chain rule, product rule, quotient rule, partial derivatives, and implicit differentiation.
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Thousands are searching for: "lim ⟨h_p, z_p⟩ = 0.9 and lim ⟨h_p, b_p⟩ = 0.9375"
Beyond standard calculators, these powerful utilities and AI-driven tools provide deep mathematical insights, graphing capabilities, and personalized tutoring to accelerate your learning journey and solve complex engineering problems.
Your 24/7 AI calculus tutor. Get personalized step-by-step guidance, concept explanations, and practice hints to master differentiation and complex analysis.
📱 Free EmulatorA full-featured virtual TI-84 graphing calculator emulator. Perform scientific calculations, graph multiple functions, and solve matrix or statistics problems directly in your browser.
Essential derivative calculators for everyday calculus problems and fundamental differentiation concepts. Perfect for students learning basic calculus, these free tools cover polynomial derivatives, power rule applications, and foundational differentiation techniques with detailed step-by-step solutions.
Solve definite and indefinite integrals with steps. Find antiderivatives and calculate area under curves instantly.
🎮 Play NowGuess the derivative of the day in this Wordle-style math game. Build your streak and master calculus through gamification.
⭐ Most PopularCalculate derivatives of any function with comprehensive step-by-step solutions. Supports all differentiation rules including chain rule, product rule, and quotient rule applications.
Apply the chain rule to composite functions with detailed explanations. Perfect for nested functions like sin(x²) or e^(3x).
Differentiate products of functions using the (f·g)' = f'g + fg' formula. Essential for calculus students learning multiplication of functions.
Calculate derivatives of rational functions using the quotient rule (u/v)' = (u'v - uv')/v². Perfect for fraction derivatives.
⭐ RecommendedBuild professional math formulas with a visual toolbar and real-time KaTeX rendering. Copy code or download PNG.
🔥 HotSolve calculus limits step-by-step. Handles and explains indeterminate forms like 0/0 and ∞/∞ using L'Hôpital's Rule and more.
Specialized derivative calculators for higher-level calculus and multivariable functions. These advanced tools handle complex differentiation including partial derivatives, implicit differentiation, directional derivatives, and vector calculus applications with comprehensive step-by-step solutions.
Find partial derivatives for multivariable functions with detailed solutions. Essential for Calculus III and multivariable calculus courses.
Solve implicit differentiation problems where y is not explicitly defined as a function of x. Perfect for equations like x² + y² = 25.
Calculate second, third, fourth, and nth order derivatives with step-by-step solutions. Essential for understanding acceleration and concavity.
Calculate derivatives in any specified direction using direction vectors. Perfect for multivariable calculus and vector calculus applications.
Compute Taylor & Maclaurin series expansions instantly with step-by-step solutions, interactive graphs, and convergence analysis.
Find the gradient vector (∇f) of multivariable scalar functions. Essential for optimization problems and vector calculus courses.
Expand complex functions into Laurent series. Analyze residues, singularities, and regions of convergence for complex analysis and contour integration.
Dedicated derivative calculators for specific types of mathematical functions. These specialized tools handle trigonometric derivatives, exponential functions, logarithmic differentiation, inverse functions, and parametric equations with precision and detailed step-by-step explanations.
Specialized tool for derivatives of trigonometric functions including sin, cos, tan, sec, csc, and cot with their combinations and compositions.
sin(x) cos(x) tan(x)Calculate derivatives of logarithmic functions including natural logarithm ln(x) and common logarithm log(x) with step-by-step solutions.
ln(x) log(x)Differentiate exponential functions like e^x, a^x, and complex exponential expressions with detailed explanations and solution steps.
e^x a^xFind derivatives of inverse functions using the inverse function theorem. Perfect for understanding inverse trigonometric and inverse exponential functions.
f⁻¹(x) Inverse TheoremCalculate dy/dx for parametric equations where both x and y are functions of parameter t. Essential for calculus BC and advanced mathematics.
x(t) y(t) dy/dxEvaluate the derivative at a specific x-value to find instantaneous rate of change. Perfect for finding slopes of tangent lines and velocity problems.
f'(a) Point Evaluation ✨ NEWInteractive tool to visualize the tangent line to any function. Move the point along the curve to see the derivative change in real-time.
Visual Explorer Tangent Slope InteractiveProfessional-grade tools for linear algebra and vector calculus. These calculators provide step-by-step solutions for eigenvalues, matrix operations, vector orthogonalization, and fundamental linear algebra concepts used in advanced engineering and data science.
Find eigenvalues and eigenvectors of square matrices. Essential for system analysis, stability theory, and advanced linear algebra applications.
Transform a set of vectors into an orthonormal basis using the Gram-Schmidt process. Perfect for orthogonalization and inner product space problems.
Perform complex matrix operations including multiplication, inversion, and determinant calculation with detailed intermediate steps.
Calculate dot product, cross product, magnitude, and unit vectors. Essential tool for physics, engineering, and 3D space calculations.
Compute Fourier transforms and analyze signal frequencies. Ideal for engineering, physics, and signal processing applications with detailed visualizations.
A derivative calculator is an advanced mathematical tool that automatically computes the rate of change of a function with respect to a variable. Our comprehensive suite of free derivative calculators uses sophisticated algorithms to find derivatives instantly, whether you're working with simple polynomial functions, complex trigonometric expressions, exponential equations, or composite functions requiring the chain rule.
In calculus, the derivative represents the instantaneous rate of change of a function. It's the foundation for understanding rates of change in physics (velocity and acceleration), economics (marginal cost and marginal revenue), engineering (optimization and stress analysis), and countless other applications. Our derivative calculator with steps not only provides the answer but shows you exactly how the solution was derived - making it the perfect learning tool for students, educators, and professionals.
Unlike basic calculators that only compute numerical values, our online derivative calculator performs symbolic mathematics. This means it works with variables, functions, and formulas - giving you exact mathematical expressions as results. Whether you need to differentiate x², sin(x), e^x, or complex expressions like (x² + 3x)·sin(2x), our calculus calculator processes them all with comprehensive step-by-step explanations that help you understand the underlying principles.
Enhance your calculus knowledge with these trusted educational resources from leading institutions:
With 15+ specialized derivative calculators available, choosing the right tool ensures accurate results and optimal learning. Follow our comprehensive guide to select the perfect calculator for your specific calculus problem:
The first step in choosing a derivative calculator is identifying what type of function you're working with:
Different derivative calculators are optimized for different course levels:
| Calculator Type | Best For | Function Examples | Course Level |
|---|---|---|---|
| Basic Derivative | General purpose, all standard functions | x², 3x + 5, sin(x), e^x | Calculus I |
| Chain Rule | Composite/nested functions | sin(x²), e^(3x), ln(2x + 1) | Calculus I |
| Product Rule | Multiplied functions | x·sin(x), (x² + 1)·e^x | Calculus I |
| Quotient Rule | Divided functions, rational expressions | (x² + 1)/x, sin(x)/cos(x) | Calculus I |
| Partial Derivative | Multivariable functions | f(x,y) = x²y + xy² | Calculus III |
| Implicit Differentiation | Implicit equations | x² + y² = 25, x³ + y³ = 6xy | Calculus I/II |
| Limit Calculator | Indeterminate forms, one-sided limits | lim x→0 sin(x)/x, lim x→∞ e^x/x | Calculus I |
| Tangent Line Explorer | Visualizing derivatives, slopes, and instantaneous rates | f(x) = x², f(x) = sin(x) | Calculus I |
In a market flooded with derivative calculators, DerivativeCalculus.com stands out as the premier choice for students, educators, and professionals. Here's why thousands of users trust our free derivative calculator suite:
Unlike competitors like Symbolab, Mathway, or Wolfram Alpha that charge for step-by-step solutions or limit free calculations, all our derivative calculators are 100% free with unlimited usage. No hidden paywalls, no premium tiers, no trial periods. We believe quality education should be accessible to everyone, which is why we've committed to keeping all features free forever.
Every derivative calculator on our platform provides detailed, step-by-step solutions that explain:
Our calculators aren't just answer machines - they're learning tools. Each calculation includes:
| Feature | DerivativeCalculus.com | Symbolab | Mathway | WolframAlpha |
|---|---|---|---|---|
| Free Step-by-Step Solutions | ✓ | Registration Required | Registration Required | ✓ |
| Practice Problems Included | ✓ | ✗ | ✗ | ✗ |
| Video Tutorials | ✓ | ✗ | ✗ | ✗ |
| Downloadable Worksheets | ✓ | ✗ | ✗ | ✗ |
| Ad-Free Experience | ✓ | Ads Present | Ads Present | Ads Present |
| Mobile Optimized | ✓ | ✓ | ✓ | Limited |
| Specialized Calculators (16+) | ✓ | Limited | Limited | Limited |
| Educational Blog & Guides | ✓ | ✗ | ✗ | ✗ |
Join thousands of satisfied students who have mastered calculus with our free derivative calculators. No credit card required, no email needed - just instant access to professional-grade calculus tools.
Derivative calculators are specialized mathematical tools that automatically compute the derivative (rate of change) of functions. They use differentiation rules like power rule, chain rule, product rule, and quotient rule to find derivatives instantly while showing step-by-step solutions that help students understand the differentiation process.
Yes! All our derivative calculators are 100% free forever with unlimited calculations. Unlike Symbolab or Mathway that charge $9.99-$19.99/month for step-by-step solutions, we provide everything completely free including detailed explanations, practice problems, video tutorials, and downloadable worksheets.
Our derivative calculator suite handles all calculus derivatives including: basic polynomial derivatives, trigonometric functions (sin, cos, tan), exponential functions (e^x), logarithmic functions (ln, log), composite functions (chain rule), products (product rule), quotients (quotient rule), implicit differentiation, partial derivatives, parametric derivatives, and higher-order derivatives (f'', f''', f⁽ⁿ⁾).
Our calculators use the professional-grade math.js library, providing 100% mathematically accurate results. The same computational engines are used in university research and industry applications. All results are symbolically exact, not numerical approximations.
No account needed! Unlike Symbolab or Mathway that require registration, our derivative calculators work instantly without sign-up. Just enter your function and get immediate results. We respect your privacy and don't store or track your calculations.
Choose based on function type: Basic Derivative Calculator for simple functions, Chain Rule Calculator for composite functions, Product Rule Calculator for multiplied functions, Quotient Rule Calculator for fractions, Partial Derivative Calculator for multivariable functions, and Implicit Differentiation Calculator when y is not explicitly defined.
Absolutely! Every derivative calculator provides detailed step-by-step solutions showing: which differentiation rule was applied, how to simplify expressions, intermediate steps, and final simplified answers. This helps you learn the process, not just get answers.
Our calculators are perfect for checking homework answers and understanding solution methods. We recommend solving problems yourself first, then using our derivative calculator to verify and learn from the step-by-step explanations. For exams, use them for practice preparation but follow your instructor's calculator policies during actual tests.
Yes! All our derivative calculators are fully optimized for mobile devices including smartphones and tablets. The responsive design ensures perfect functionality on any screen size. Calculate derivatives anywhere, anytime without downloading apps.
Unlike Symbolab, Mathway, or WolframAlpha that charge for features, all our calculators are free forever including step-by-step solutions. We offer 15+ specialized calculators, comprehensive tutorials, practice problems, video lessons, and downloadable worksheets - features competitors don't provide. Plus, no registration, no ads, and complete privacy protection.
Our calculators provide educational value through: detailed step-by-step explanations showing every stage of differentiation, identification of which rules were applied and why, visual representations when helpful, links to relevant tutorials and lessons, practice problems for reinforcement, and real-world applications showing where derivatives are used.
Yes! Use the "Copy Result" button to copy calculations to your clipboard, the "Share" button to send to classmates or instructors, or print the page (Ctrl+P / Cmd+P) to save as PDF. We're developing direct PDF export features coming soon.
Still have questions? Visit our comprehensive FAQ page or contact our support team for personalized assistance with your calculus learning journey.
Master calculus with our comprehensive suite of derivative tools. Follow these simple steps to calculate any derivative instantly with step-by-step solutions.
Determine if you have a basic polynomial, composite function requiring chain rule, product of functions, quotient, or multivariable function to choose the optimal calculator.
Choose from Basic Derivative, Chain Rule, Product Rule, Quotient Rule, Partial Derivative, Implicit Differentiation, or any of our 15+ specialized calculators.
Input your function using proper mathematical notation: x^2 for x squared, sin(x) for sine, e^x for exponential, ln(x) for natural log. Remember to use * for multiplication (2*x not 2x).
Examine the detailed solution to understand the differentiation process, including which rules were applied, simplification steps, and the final derivative.
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