Derivatives in depth

Question 1

Derivative of arcsin

Answer 1

1 / (sqrt 1- u ^2)

Question 2

Derivative of arccos

Answer 2

-1 / (sqrt 1- u^2)

Question 3

Derivative of arctan

Answer 3

1 / (u^2 + 1)

Question 4

Derivative of arccot

Answer 4

-1 / (u^2 + 1)

Question 5

Derivative of arcsec

Answer 5

1 / ( |u| * sqrt (u^2 - 1) )

Question 6

Derivative of arccsc

Answer 6

-1 / ( |u| * sqrt(u^2 - 1) )

Question 7

Pythagorean theorum

Answer 7

a^2 + b^2 = c^2

Question 8

Distance formula

Answer 8

sqrt ( x2 - x1 )^2 + ( y2 - y1 )^2

Question 9

Circumference formula

Answer 9

2 * pi * r

Question 10

Area formulas

Answer 10

Square = b * h
Circle = pi * r^2

Question 11

Volume formulas

Answer 11

Square = b * h * w
Cylinder = pi * r^2 * h

Question 12

SohCahToa

Answer 12

Sin = opp / hyp
Cos = adj / hyp
Tan = opp / adj

Question 13

How to find extrema

Answer 13

Set derivative equal to zero
Use sign chart (relative) or candidates test (absolute)

Question 14

L’Hopitals rule

Answer 14

Used when you get indeterminate form ( 0/0 or infinity over infinity)
Other forms: 0 * infinity , infinity - infinity , 0 * 0 , infinity * 1