Derivative Calculator

Enter Function

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