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) = log3 x – 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
-sin2 x
cos2x – sin2x
1
Q. The "quotient rule" states that the derivative of the function 
is equal to
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
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