Calculus 1 Differentiation Rules

Derivative of a Constant

f’(c ) = 0

Power Rule

f’(xⁿ) = nx^n-1

The Constant Multiple Rule

f’(cf(x)) = cf’(x)

Sum Rule

d/dx [f(x)+g(x)] = f’(x) + g’(x)

Difference Rule

d/dx [f(x)-g(x)] = f’(x) - g’(x)

Derivative of the Natural Exponential Function

f’(e^x) = e^x

The Product Rule

p’(x) = f’(x)g(x) + f(x)g’(x)

The Quotient Rule

for q(x) = f(x)/g(x): q’(x) = [f’(x)g(x) - f(x)g’(x))]/ [g(x)]²

Derivative of General Exponential Functions

f’(b^x) = b^xlnb

Derivative of the natural logarithmic function

Derivative of the natural logarithmic function w/ chain rule

Derivative of a logarithmic function