formula quizzes updated

d/dx (sin x)

cos x

inverse function formula

d/dx (cos x)

-sin x

d/dx (tan x)

sec²x

d/dx (csc)

( -csc x ) ( cot x )

d/dx (sec x)

(sec x ) (tan x)

d/dx (cot x)

-csc²x

d/dx (e^x)

e^x

d/dx (ln x) 

1/x

d/dx (a^x)

d/dx (loga x)

d/dx (f/g) — quotient rule

d/dx (fg)

chain rule: if h(x) = f(g(x)), then

tan x =

sin x / cos x

quotient ID

cot x =

cos x / sin x

quotient ID

sec x =

1 / cos x

reciprocal ID

csc x =

1 / sin x

reciprocal ID

sin²x + cos²x = 1. what is the other pythagorean ID?

sec²x - tan²x = 1. what is the other pythagorean ID?

2sinxcosx = sin2x. what is the other double angle ID?

cos²x - sin²x = cos2x. what is the other double angle ID?

sin (-x) = -sin x (odd), cos(-x) = cos x (even), tan (-x) = -tanx (odd)

even-odd id’s

definition |x|

sin (A + B) =

sin A cos B + cos A sin B

cos (A + B) =

cos A cos B - sin A sin B

sin (A - B) =

sin A cos B - cos A sin B

cos (A-B)

cos A cos B + sin A sin B

distance between two points

midpoint formula

laws of logarithms ln(ab)=

ln (ab) = ln a + ln b

laws of logarithms ln (a/b)

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

laws of logarithms (a^n)

ln (a^n) = n ln a

ln (1/a) =

-ln a

ln (0) =

undefined

ln (1)=

0

ln (e)=

1

THE UNIT CIRCLE :)

cos is the x value and sin is the y value

one sided limits

definition of a limit

lim x→a of c =

c

average rate of change…

squeeze theorem

limit rules for e^x

limit rules for ln x

rules for lim 1/x

lim(x→0) of sinx/x =

1

lim(x→0) of 1-cosx/x =

0

limit rules for arctan x

definition of vertical asymptote

definition of horizontal asymptote

definition of continuity

intermediate value theorem (IVT):

definition of the derivative

tangent line equation

normal line

the line perpendicular to the tangent line at the point of tangency

three reasons a function f will not be differentiable at a point x=a

important derivatives

the derivative of the inverse of sin x

the derivative of the inverse of cos tx

the derivative of the inverse of tan x

the derivative of the inverse of cot x

the derivative of the inverse of sec x

the derivative of the inverse of csc x