Calculate Function Derivatives
Enter your function in the box below using standard mathematical notation.
Derivative Result:
Your derivative will appear here
Step-by-Step Solution:
Explanation will appear here
Derivative Calculator - Find Derivatives of Functions Instantly
Our powerful derivative calculator helps you find derivatives of mathematical functions quickly and accurately. Whether you're a student learning calculus or a professional needing quick solutions, this tool provides step-by-step derivatives for any valid function.
Our powerful derivative calculator helps you find derivatives of mathematical functions quickly and accurately. Whether you're a student learning calculus or a professional needing quick solutions, this tool provides step-by-step derivatives for any valid function.
How to Use the Derivative Calculator
Simply enter your function using standard mathematical notation. Our calculator supports:
- Polynomials (x^2, x^3, etc.)
- Trigonometric functions (sin(x), cos(x), tan(x))
- Exponential functions (e^x, 2^x)
- Logarithmic functions (ln(x), log(x))
- And many more mathematical operations
Examples of Valid Inputs:
x^2 + 3*x + 2sin(x) + cos(2*x)e^(2*x) + ln(x)(x^2 + 1)/(x - 1)
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Frequently Asked Questions
What is a derivative in calculus?
A derivative represents the rate of change of a function with respect to its variable. It's a fundamental concept in calculus that measures how a function changes as its input changes.
How accurate is this derivative calculator?
Our calculator uses symbolic differentiation to provide mathematically exact results, not approximations. It applies standard differentiation rules including the power rule, product rule, quotient rule, and chain rule.
What notation does the calculator use for derivatives?
The calculator uses Leibniz notation (dy/dx) for displaying derivatives, which is the standard notation in calculus.
Understanding Mathematical Derivatives
Derivatives are fundamental to calculus and have numerous applications in physics, engineering, economics, and many other fields. They represent instantaneous rates of change and are used to solve problems involving optimization, motion, and growth.
Applications of Derivatives
Derivatives have practical applications across various disciplines:
- Physics: Velocity and acceleration are derivatives of position
- Economics: Marginal cost and revenue are derivative concepts
- Engineering: Used in control systems and signal processing
- Computer Science: Essential for machine learning algorithms and optimization
Basic Differentiation Rules
Our calculator applies these fundamental rules:
- Power Rule: d/dx[x^n] = n*x^(n-1)
- Product Rule: d/dx[f(x)*g(x)] = f'(x)*g(x) + f(x)*g'(x)
- Quotient Rule: d/dx[f(x)/g(x)] = [f'(x)*g(x) - f(x)*g'(x)]/[g(x)]^2
- Chain Rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)
