Computations

Question 1

What is the D/dx [tan x] ?

Answer 1

Sec^2 x

Question 2

What is the d/dx of [cot x]?

Answer 2

-csc^2 x

Question 3

What does -csc^2 x turn into? Since it does not exist,

Answer 3

-cot^2 x -1

Question 4

What is the d/dx of [sec x]

Answer 4

Sec x tan x

Question 5

What is the derivative of [csc x]?

Answer 5

-cscx cotx

Question 6

What is the formula of the constant rule?

Answer 6

D/dx (c)= 0

Question 7

What is the formula of the power rule?

Answer 7

D/dx (x^n) = nx^n-1

Question 8

What is the formula of the constant multiple rule?

Answer 8

D/dx (cf(x)) = cf ’(x)

Question 9

What is the formula for the sum and difference rule?

Answer 9

f ‘ (x)➖g ‘ (x)
f ’ (x) ➕ g ‘ (x)

Question 10

What is the derivative of the product rule?

Answer 10

f ‘ (x) g(x) ➕ g ‘ (x) f(x)

Question 11

What is the derivative of the quotient rule?

Answer 11

g(x) f ‘ (x) ➖ f (x) g ‘ (x) / (g(x))^2

Question 12

What is the derivative of extended power rule? (Hint: rational number)

Answer 12

nx^n-1

Question 13

What is the derivative of [sin x]?

Answer 13

Cos x

Question 14

What is the derivative of [Cos x ]?

Answer 14

-sin x

Question 15

What is the chain rule?

Answer 15

A method of finding derivatives of composite functions

Question 16

What is velocity?

Answer 16

Object moving along a line on graph. (Ex: up, down, left or right)

Question 17

What is speed?

Answer 17

Talking about how fast the object is moving on the graph

Question 18

What is acceleration?

Answer 18

The rate of change of speed in one particular direction

Question 19

What is the chain rule differentiable function of sin u?

Answer 19

Cos u

Question 20

What is the chain rule differentiable function of tan u?

Answer 20

Sec^2 u

Question 21

What is the chain rule differentiable function of sec u?

Answer 21

Sec u tan u

Question 22

What is the chain rule differentiable function of cos u?

Answer 22

—sin u

Question 23

What is the chain rule differentiable function of cot u?

Answer 23

-csc^2 u

Question 24

What is the chain rule differentiable function of csc u?

Answer 24

-csc u cot u

Question 25

What is the derivative of the inverse trig function of (sin^-1 (x))

Answer 25

1/ square root of 1➖x^2

Question 26

What is the derivative of the inverse trig function of (cot^-1 (x))

Answer 26

➖ (1/ 1+ x^2 )

Question 27

What is the derivative of the inverse trig function of (tan^-1 (x)).

Answer 27

1 /1➕ x^2

Question 28

What is the derivative of the inverse trig function of (sec^-1 (x))

Answer 28

1/ |x| square root x^2 -1

Question 29

What is the derivative of the inverse trig function of (cos^-1 (x))

Answer 29

➖( 1/ square root 1–x^2)

Question 30

What is the derivative of the inverse trig function of (sin^-1 (x))

Question 31

What is the derivative of the inverse trig function of (csc^-1 (x))

Answer 31

1/ |x| square root x^2-1