Derivatives Challenge

Question 1

What is the quotient rule formula?

Accepted Answer

(f'g - fg')/g^2

Question 2

What is the derivative of f(x) = 1/x4?

Accepted Answer

-4x^{-5}

Question 3

Which of the following functions requires both the power rule and the quotient rule?

Accepted Answer

f(x) = (x^2 + 1)/x^3

Question 4

What is the derivative of f(x) = 1/x?

Accepted Answer

-x^{-2}

Question 5

What is the derivative of f(x) = x5?

Accepted Answer

5x^4

Question 6

What is the derivative of f(x) = x-2?

Accepted Answer

-2x^{-3}

Question 7

What is the derivative of f(x) = 5/x2?

Accepted Answer

-10x^{-3}

Question 8

What is the derivative of f(x) = x^2 / (x+1)?

Accepted Answer

What is the derivative of f(x) = x^2 / (x+1)?

Question 9

If f(x) = (2x^3 + 5x)/x^2, what's the simplest first step before applying derivative rules?

Accepted Answer

Rewrite the function as a sum of powers

Question 10

Let f(x) = x^2 / (x+1). What rule do you use to find f'(x)?

Accepted Answer

Quotient Rule

Question 11

What is the power rule for derivatives?

Accepted Answer

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

Question 12

The derivative of xn, using the power rule, requires what condition on n?

Accepted Answer

Any real number

Question 13

What is the derivative of f(x) = 7x3?

Accepted Answer

21x^2

Question 14

What is the derivative of f(x) = (x^3 + 1)/x^2?

Accepted Answer

(3x^2 x^2 - (x^3 + 1)(2x))/x^4

Questions 14