# Computing Derivatives: Embrace Your Inner Calculator Quiz

Think you’ve got your head wrapped around Computing Derivatives? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. Let f(x) = 4g(x). If g ' (x) = 2x, what is the derivative of f(x)?

f ' (x) = 2x

f ' (x) = 4x

f ' (x) = 8x

f ' (x) = 4x2

Q. Which of the following expressions is not equivalent to the others?

2log3 x

(log3 x)2

Q. Find the derivative of f(x) = log7 x + 7x.

Q. Find the derivative of f(x) = logx – cos x.

Q. The "product rule" states that the derivative of the function f · g is

f 'g + fg '

f'g'

f'g' + fg

f'g'fg

Q. Find the derivative of f(x) = sin x cos x.

sin2 x

-sinx
cos2x – sin2x

1
Q. The "quotient rule" states that the derivative of the function  is equal to

Q. Find the derivative of the function

Q. The derivative of cot x is

csc2 x

-csc2x

csc x · cot x

-csc x · cot x

Q. Finding the derivative of the function without rewriting the function first, requires

one use of the product rule and one use of the quotient rule
one use of the product rule and two uses of the quotient rule
two uses of the product rule and one use of the quotient rule
two uses of the product rule and two uses of the quotient rule