# 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

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