AP AB Calculus Formula Review

This has all the formulas that we went over in class :) If I'm missing any just let me know!

Derivative Standard Form

Derivative Alternate Form

Power Rule

Product Rule

Quotient Rule

Chain Rule

Mean Value Theorem

Newton’s Method

Reiman Sums

Average Value of a Function

Compound Interest

Infinite Compound Interest

Euler’s Method

The growth of a population grows proportionately to the size of the population

Law of Exponential Growth

dP/dt = KP

Exponential Growth

dT/dt =K(T-T_o )

T=T_s + (T_o - T_s )e^kt

Newton’s Law of Cooling

dP/dt = KP (1-P/L)

L= Carrying Capacity

P=L/(1+be^-kt ) b= (L-P₀ )/ P₀

Logistics Formula

Area Between Curves

Volume

Arc Length

Surface Area

Work

Force= kd

Hooke’s Law

|velocity| =

Speed

Average Rate of Change

Instantaneous rate of change is

a derivative

Derivative of Position

Velocity

Derivative of Velocity

Acceleration

Antiderivative of Velocity

Position

Derivative of cos(x)

-sin(x)

Derivative of sin(x)

cos(x)

Derivative of tan(x)

sec²(x)

Derivative of sec(x)

sec(x)tan(x)

Derivative of csc(x)

-csc(x)cot(x)

Derivative of cot(x)

-csc²(x)

Derivative of y=a^x

a^xln(a)

Derivative of f(x)= log_ax

1/(xln(a))

Derivative of ln(x)

1/x

Derivative of tan^-1(x)

1/(1+x²)

Derivative of sin^-1(x)

1/√(1-x²)

Derivative of sec^-1(x)

1/(x√(x²-1))

Derivative of cot^-1(x)

-1/(1+x²)

Derivative of cos^-1(x)

-1/√(1-x²)

Derivative of csc^-1(x)

-1/(x√(x²-1))

∫cos(x)dx

sin(x)+c

∫sin(x)dx

-cos(x)+c

∫tan(x)dx

-ln|cos(x)|+c

∫cot(x)dx

ln|sin(x)|+c

∫sec(x)dx

ln|sec(x)+tan(x)|+c

∫csc(x)dx

-ln|csc(x)+cot(x)|+c

∫a^xdx

a^x/ln(a) +c

∫1/√(a²-x²)dx

sin^-1(x/a) +c

∫1/(a²+x²)dx

1/a tan^-1(x/a) +c

∫1/√(a²-x²)dx

1/a sec^-1(|x|/a) +c

sin²(x)+cos²(x)=1

1+tan²(x)=sec²(x)

1+cot²(x)=csc²(x)

Pythagorean Identities

sin(x)=1/csc(x)

cos(x)=1/sec(x)

tan(x)=1/cot(x)

csc(x)=1/sin(x)

sec(x)=1/cos(x)

cot(x)=1/tan(x)

Reciprocal Identities

=1

=0