Understanding Derivatives

Derivatives measure how a function changes as its input changes, representing instantaneous rates of change. They're fundamental in physics for motion analysis, in economics for marginal concepts, and in machine learning for optimization.

Step-by-Step Guide

Enter your function using standard mathematical notation (e.g., x^2, sin(x), ln(x))
Optionally provide a specific point to evaluate the derivative
Click calculate to see both symbolic derivative and numerical value
Use reset to clear all inputs and results

Examples

Double: f(x) = 2x → f'(x) = 2
Quadratic: f(x) = x² → f'(x) = 2x
Exponential: f(x) = e^x → f'(x) = e^x

Reference Table

Function	Derivative
x^n	nx^(n-1)
sin(x)	cos(x)
cos(x)	-sin(x)
e^x	e^x
ln(x)	1/x

Warning: This calculator uses numerical methods for evaluation. Results may vary slightly from exact symbolic derivatives due to floating-point precision limitations.

Derivative Calculator

Results

Understanding Derivatives

Step-by-Step Guide

Examples

Reference Table

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Frequently Asked Questions

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Derivative Calculator - Symbolic and Numeric Help

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