Derivative CalculatorDerivative Calculator
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Derivative Calculator with Steps & Interactive Graphing

Solve derivatives instantly with our advanced symbolic differentiation engine. Whether you're a student checking homework or a professional needing quick gradient computations, get step-by-step solutions for algebraic, trigonometric, and exponential functions.

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Step-by-step differentiation with interactive graphs

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Master Calculus with a Professional Derivative Calculator

Master Calculus with a Professional Derivative Calculator

Derivatives are the fundamental tool of calculus, representing the instantaneous rate of change of a function. However, manual differentiation can be tedious and prone to errors, especially when dealing with nested functions or complex products. Our tool bridges the gap between theoretical understanding and practical application.

  • Transparent Methodology
    Unlike black-box calculators, we reveal the 'why' behind the 'what'. By showing intermediate steps—like how the Product Rule splits terms or how the Chain Rule handles inner functions—we reinforce your learning process.
  • Visual Intuition
    Calculus is geometric. Our dynamic graphing engine plots both f(x) and f'(x) simultaneously, allowing you to visually verify that the derivative is positive where the function increases and zero at extrema.
  • Comprehensive Rule Coverage
    From the basic Power Rule to logarithmic differentiation and inverse trigonometric derivatives, our engine is tested against deterministic symbolic math baselines to ensure consistent results.
Benefits

Why Academic Professionals Trust This Tool

Accuracy and clarity are paramount in mathematics. We prioritized these pillars to create a derivative calculator that serves as a reliable companion for your academic and professional journey.

Stop getting stuck on algebraic simplification. Use our tool to verify your manual work instantly, identify exactly where you made a mistake, and correct your understanding of differentiation rules.

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How to Use the Derivative Calculator Effectively

Follow these steps to get the most out of your differentiation tasks:

Advanced Computational Features

A robust set of tools designed for serious mathematical work.

Symbolic Math Engine

Powered by advanced algorithms that treat mathematical expressions as tree structures, allowing for exact manipulation and differentiation rather than numerical approximation.

Intelligent Simplification

The system automatically simplifies results (e.g., combining like terms, applying trig identities) to present the most readable form, while maintaining mathematical equivalence.

Dual-Mode Graphing

Plots the original function f(x) and its derivative f'(x) on the same canvas with auto-scaling axes, making it easy to spot relationships like local maxima/minima (where f'(x)=0).

LaTeX & MathML Support

Seamless integration with academic writing standards. One-click copy for LaTeX code ensures your workflow from calculation to documentation is frictionless.

Responsive Performance

Optimized client-side computation keeps derivatives fast in your browser, without sending your expression to a server.

Multi-Variable Support

Supports single-variable differentiation today, and is designed to expand toward partial derivatives and more advanced calculus workflows.

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Our derivative calculator is the go-to tool for students worldwide.

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Essential Derivative Rules Reference

A quick guide to the fundamental theorems used by our calculator engine.

Power Rule

The Power Rule is used to differentiate functions of the form f(x) = x^n, where n is a real number. It states that you bring the exponent down to multiply with the coefficient and subtract one from the exponent.

ddxxn=n⋅xn−1\frac{d}{dx} x^n = n \cdot x^{n-1}
ExampleIf f(x)=x3, then f′(x)=3x2.\text{If } f(x)=x^3, \text{ then } f'(x)=3x^2.

Product Rule

The Product Rule is used when differentiating a product of two functions, u(x) and v(x). It states that the derivative is the first function times the derivative of the second, plus the second function times the derivative of the first.

ddx[u(x)⋅v(x)]=u′(x)v(x)+u(x)v′(x)\frac{d}{dx} [u(x) \cdot v(x)] = u'(x)v(x) + u(x)v'(x)
ExampleIf f(x)=xsin⁡(x), then f′(x)=sin⁡(x)+xcos⁡(x).\text{If } f(x)=x\sin(x), \text{ then } f'(x)=\sin(x)+x\cos(x).

Quotient Rule

The Quotient Rule is applied when differentiating a ratio of two functions, u(x)/v(x). It is often remembered by the rhyme: 'Low d-High minus High d-Low, over the square of what's below'.

ddx[u(x)v(x)]=u′(x)v(x)−u(x)v′(x)[v(x)]2\frac{d}{dx} \left[ \frac{u(x)}{v(x)} \right] = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}
ExampleIf f(x)=sin⁡(x)x, then f′(x)=xcos⁡(x)−sin⁡(x)x2.\text{If } f(x)=\frac{\sin(x)}{x}, \text{ then } f'(x)=\frac{x\cos(x)-\sin(x)}{x^2}.

Chain Rule

The Chain Rule is used for differentiating composite functions, f(g(x)). It states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

ddxf(g(x))=f′(g(x))⋅g′(x)\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)
ExampleIf h(x)=(3x+1)2, then h′(x)=6(3x+1).\text{If } h(x)=(3x+1)^2, \text{ then } h'(x)=6(3x+1).
FAQ

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