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