Derivative Calculator
Find the derivative of common functions. This calculator supports basic polynomial and trigonometric functions.
Function Input
Understanding Derivatives
The derivative of a function represents the rate of change of a function with respect to a variable. It is a fundamental concept in calculus with wide applications in science, engineering, and economics.
Basic Differentiation Rules:
- Power Rule: d/dx(xn) = nxn-1
- Constant Rule: d/dx(c) = 0
- Constant Multiple Rule: d/dx(cf(x)) = c * d/dx(f(x))
- Sum/Difference Rule: d/dx(f(x) ± g(x)) = d/dx(f(x)) ± d/dx(g(x))
- Derivative of sin(x): d/dx(sin(x)) = cos(x)
- Derivative of cos(x): d/dx(cos(x)) = -sin(x)
Table of Common Derivatives
| Function f(x) | Derivative f'(x) |
|---|---|
| c (constant) | 0 |
| x | 1 |
| xn | nxn-1 |
| ex | ex |
| ln(x) | 1/x |
| sin(x) | cos(x) |
| cos(x) | -sin(x) |
| tan(x) | sec2(x) |
Frequently Asked Questions
What is a derivative?
In calculus, the derivative of a function of a real variable measures the sensitivity of change of the function value (output value) with respect to a change in its argument (input value). It is a fundamental tool in calculus.
What are the basic rules of differentiation?
Basic rules include the power rule (d/dx(x^n) = nx^(n-1)), constant rule (d/dx(c) = 0), sum/difference rule, product rule, quotient rule, and chain rule.
What are derivatives used for?
Derivatives are used to find the slope of a tangent line to a curve, determine rates of change (e.g., velocity, acceleration), optimize functions (find maximum/minimum values), and analyze the behavior of functions.