Calculus: Implicit Derivatives & Related Rates

Question 1

What is the derivative of r^2 with respect to time? (Note ^ will be used to denote exponents. r^2 means r squared)

Accepted Answer

2r(dr/dt)

Question 2

What is the derivative of x^3 with respect to x?

Accepted Answer

3 x^2

Question 3

A circular puddle evaporates. The perimeter decreases by 1 cm/min. How is radius changing? P=2 pi r

Accepted Answer

-1/(2 pi) cm/min

Question 4

dA/dt, the change in area over the change in time might have which of the following units

Accepted Answer

square meters / second

Question 5

Area of a square increases by 3 m/hour. How fast is the side length changing when the side length is 6? A=s^2

Accepted Answer

1/4 m/hr

Question 6

What is the derivative of sin(theta) with respect to theta?

Accepted Answer

cos(theta)

Question 7

A circular puddle evaporates. The radius decreases by 2 cm/min. How is area changing when radius is 7? A=pi r^2

Accepted Answer

-28 pi square cm/min

Question 8

dr/dt the change in radius over the change in time might have which of the following units

Accepted Answer

meters / second

Question 9

What is the derivative of ab with respect to time t?

Accepted Answer

(da/dt)b + a(db/dt)

Question 10

What is the derivative of x^3 with respect to time t?

Accepted Answer

3 x^2 (dx/dt)

Question 11

Area might have which of the following units

Accepted Answer

square meters

Question 12

What is the derivative of xy with respect to x?

Accepted Answer

y + x(dy/dx)

Question 13

What is the derivative of cos(theta) with respect to time t?

Accepted Answer

-sin(theta)(dtheta/dt)

Question 14

What is the derivative of a^2 + b^2 with respect to time t?

Accepted Answer

2a (da/dt) + 2b (db/dt)

Questions 14