0 - Mathematics

Question 1

What is the derivative of ln(x)?

Answer 1

1/x = x⁻¹

Question 2

What is the derivative of sin(x)?

Answer 2

cos(x)

Question 3

What is the derivative of cos(x)?

Answer 3

-sin(x)

Question 4

What is the derivative of eˣ?

Answer 4

eˣ

Question 5

What is the derivative of tan(x)?

Answer 5

sec²(x)

Question 6

What is the derivative of sec(x)?

Answer 6

sec(x)tan(x)

Question 7

What is the derivative of aˣ?

Answer 7

aˣln(a)

Question 8

What is the derivative of logₐ(x)?

Answer 8

1 / [ x ln(a) ]

Question 9

What is the derivative of 1/x ?

Answer 9

• 1/x²

Question 10

How can you maximize an exponential utility function?

Answer 10

Take the logarith of it

Question 11

What is the logarithmic form of the C.-D. production function?
-> u₁(x₁₁, x₂₁) = x₁₁ª x₂₁¹⁻ª

Answer 11

ln u₁ = α ln x₁₁ + (1-α) ln x₂₁

Question 12

Apply the product rule to transform the following logarithm: ln(x ∙ y) = ?

Answer 12

ln(x) + ln(y)

Question 13

Apply the quotient rule to transform the following logarithm: ln(x / y) = ?

Answer 13

ln(x) - ln(y)

Question 14

Apply the power rule to transform the following logarithm: ln(xʸ) = ?

Answer 14

y ∙ ln(x)

Question 15

Take the derivative w.r.t. b:

(a + b)²

Answer 15

2(a+b)

Question 16

Take the derivative w.r.t. b:

-(a + b)²

Answer 16

-2(a+b)

Question 17

Take the derivative w.r.t. b:

(a - b)²

Answer 17

-2(a-b)

Question 18

Take the derivative w.r.t. b:

-(a - b)²

Answer 18

2(a-b)