Derivatives

Introduction to Derivatives

Derivatives are mathematical tools for measuring the rate of change of a function. This page provides tools for calculating derivatives of functions from basic to complex.

Calculate Derivatives

f(x) = x² + 3x + 1

Calculate Derivative Value at Point

Basic Derivative Rules

Power Function

f(x) = xⁿ

f'(x) = n·xⁿ⁻¹

Exponential Function

f(x) = eˣ

f'(x) = eˣ

Logarithmic Function

f(x) = ln(x)

f'(x) = 1/x

Sine Function

f(x) = sin(x)

f'(x) = cos(x)

Cosine Function

f(x) = cos(x)

f'(x) = -sin(x)

Tangent Function

f(x) = tan(x)

f'(x) = 1/cos²(x)

Product Rule

(u·v)' = u'·v + u·v'

Quotient Rule

(u/v)' = (u'·v - u·v')/v²

Chain Rule

[f(g(x))]' = f'(g(x))·g'(x)