AP Calculus AB Study Guide Quarter Exam

Derivative of sin(x)
cos(x)

Derivative of cos(x)
-sin(x)

Derivative of tan(x)
sec^2(x)

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

Derivative of cot(x)
-csc^2(x)

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

Limits of infinity with highest exponent on top
-/+ infinity

Limits of infinity with highest exponent on bottom

Limits of infinity with same highest exponent
coefficents

Tangent lines
slope/ derivative

Intermediate value theorem
for each value between the least upper bound and greatest lower bound of the image of a continuous function there is at least one point in its domain that the function maps to that value.

Normal Line
Perpendicular (opposite/ reciprocal slope)

Derivatives of Inverse Trig: tan^-1(x)
(1/(x^2+1))

Derivatives of Inverse Trig: sin^-1(x)
(1/((1-x^2)^(1/2))

Derivatives of Inverse Trig: sec^-1(x)
(1/(lxl (x^2-1)^(1/2))

Derivatives of Inverse Trig:cos^-1(x)
-(1/((1-x^2)^(1/2))

Derivatives of Inverse Trig: cot^-1(x)
-(1/(x^2+1))

Derivatives of Inverse Trig: csc^-1(x)
-(1/(lxl (x^2-1)^(1/2))

Derivative of e^x
e^x

Derivative of 5*x
(5^x) (ln 5)

Velocity
s'(x)

Acceleration
s”(x)

Derivatives of Inverse Functions
1 over (x) replaced with y

Implicit Differentiation
Not solved for y. Must use (dy/dx)

Differentiation of Natural Log
1 over

Not differntiable
cusp, corner, hole

Parallel Tangent
same slope

Horizontal Tangent
deriviative = 0

Vertical Tangent
derivative = undefined