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)