Calculus AB Unit 2 Rules & Processes

Average Rate of Change/Slope of Secant Line (2 Formulas)

Instantaneous Rate of Change/Slope of Tangent Line (2 Formulas)

Also the Definition of the Derivative, or f’(x)

Equation of the Tangent Line

aka Point-Slope Form

Constant Rule

d/dx (Constant) = 0

Power Rule

d/dx (axⁿ) = naxⁿ⁻¹

Sum-Difference Rule

d/dx [f(x) + g(x)] = f'(x) + g'(x)

Product Rule

d/dx [f(x)*g(x)] = f(x)g'(x) + f'(x)g(x)

Quotient Rule

d/dx [f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)²]

Derivative of Sin

d/dx sin(x) = cos(x)

Derivative of Cos

d/dx cos(x) = -sin(x)

Derivative of Tan

d/dx tan(x) = sec²(x)

Derivative of Sec

d/dx sec(x) = sec(x)tan(x)

Derivative of Cot

d/dx cot(x) = -csc²(x)

Derivative of Csc

d/dx csc(x) = -csc(x)cot(x)

Chain Rule

d/dx [f(g(x)] = f'(g(x))*g'(x)

Exponential Func. Rule

d/dx eⁿ = n'(eⁿ)

Natural Log Func. Rule

d/dx ln x = 1/x

Limit Definition

lim (h→0) = [f(x+h) - f(x)]/[h]

Alt. Limit Definition

lim (x→a) = [f(x) - f(a)]/[x-a]