Derivative Calculator
Calculate derivatives with step-by-step solutions. Supports power rule, product rule, quotient rule, chain rule, and more.
Formula:d/dx[f(x)]
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f(x)
Derivative Practice Problems
Test your skills with practice problems
Practice with 5 problems to test your understanding.
What is a Derivative?
A derivative is a fundamental concept in calculus that represents the instantaneous rate of change of a function. It measures how a function's output changes as its input changes, essentially finding the slope of the tangent line at any point on the curve.
The derivative of a function f(x) is denoted as f'(x), df/dx, or d/dx[f(x)]. It tells us the rate at which f(x) is changing with respect to x at any given point.
Key Facts About Derivatives
- •Derivatives measure instantaneous rate of change
- •The power rule: d/dx[x^n] = nx^(n-1)
- •The chain rule handles composite functions
- •Product rule: (fg)' = f'g + fg'
- •Quotient rule: (f/g)' = (f'g - fg')/g²
- •Common derivatives: d/dx[sin(x)] = cos(x), d/dx[e^x] = e^x
- •Higher-order derivatives are derivatives of derivatives
- •Critical points occur where the derivative equals zero
Frequently Asked Questions
How do you find the derivative of x²?
Using the power rule, d/dx[x²] = 2x. Bring down the exponent (2) as a coefficient and reduce the exponent by 1 (2-1=1), giving 2x¹ = 2x.
What is the derivative of sin(x)?
The derivative of sin(x) is cos(x). This is a standard derivative that should be memorized.
How do I use the chain rule?
The chain rule is used for composite functions: d/dx[f(g(x))] = f'(g(x)) · g'(x). Differentiate the outer function, keeping the inner function unchanged, then multiply by the derivative of the inner function.
What is the difference between dy/dx and d/dx?
dy/dx represents the derivative of y with respect to x (a specific function's derivative). d/dx is the differentiation operator that acts on whatever expression follows it.
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How this works
Formulas follow standard definitions from the NIST Digital Library of Mathematical Functions and classical textbook derivations. Calculations run entirely in your browser. Where a closed-form solution exists, it is used; where an iterative or numerical method is required, the implementation is named on the page.
Sources
- [1]NIST Digital Library of Mathematical FunctionsAcademicdlmf.nist.govAccessed Apr 21, 2026
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).