Summary AP CALC FORMULAS

AP CALC FORMULAS



Distance Formula √((x₂ - x₁)² + (y₂ - y₁)²)

Midpoint Formula ((x₁ + x₂)/2 , (y₁ + y₂)/2)

Logarithm Property ln(ab) = ln(a) + ln(b)

(Product)

Logarithm Property ln(a/b) = ln(a) - ln(b)

(Quotient)

Logarithm Property (Power) ln(aⁿ) = n ln(a)

Definition of a Limit lim f(x) = L iff left and right limits equal L

Average Rate of Change (f(b) - f(a)) / (b - a)

Derivative Definition f′(x) = lim(h→0) [(f(x+h) - f(x))/h]

Alternate Derivative f′(b) = lim(x→b) [(f(x) - f(b))/(x - b)]

Definition

Tangent Line Equation y - f(a) = f′(a)(x - a)

Product Rule (fg)′ = f′g + fg′

Quotient Rule (f/g)′ = (f′g - fg′)/g²

Chain Rule (f(g(x)))′ = f′(g(x)) · g′(x)

Derivative of sin(x) cos(x)

Derivative of cos(x) -sin(x)

Derivative of tan(x) sec²(x)

Derivative of csc(x) -csc(x)cot(x)

Derivative of sec(x) sec(x)tan(x)