# Computing Derivatives: What's in a Slope? Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Computing Derivatives**Q. Let

*f*(*x*) = e. Then*f '*(

*x*) is undefined because

*f*has no slope.

*f '*(

*x*) = 0

*f '*(

*x*) = 1

*f '*(

*x*) =

*e*

Q. What is the derivative of

*f*(*x*) = 5*x*+ 6?*f '*(

*x*) = 0

*f '*(

*x*) = 1

*f '*(

*x*) = 5

*f '*(

*x*) = 6

Q. Which of the following is not a power function?

*f*(

*x*) = x

^{-2}

*f*(

*x*) = x

^{(0.5)}

Q. For which function

*f*(*x*) is*f '*(*x*) = -3*x*^{-4}?*f*(

*x*) = x

^{-2}

*f*(

*x*) = x

^{-3}

*f*(

*x*) = x

^{-4}

*f*(

*x*) = x

^{-5}

Q. What is the derivative of

*f*(*x*) = e^{x}?*f '*(

*x*) =

*e*

^{x}

*f '*(

*x*) =

*e*

^{x}(ln

*x*)

*f '*(

*x*) =

*x*e

^{(x – 1)}

*f '*(

*x*) = 1

Q. The slope of the function

*f*(*x*) =*e*^{x}issometimes positive, sometimes negative, and sometimes 0.

always either 0 or positive.

always positive.

sometimes positive and sometimes undefined.

Q. Let

*f*(*x*) = 6^{x}. Then*f '*(

*x*) = 6

^{x}

*f '*(

*x*) = 6

^{x}(ln 6)

*f '*(

*x*) = 6

*x*ln 6

*f '*(

*x*) = (ln 6)

^{x}

Q. Which function

*f*(*x*) has the derivative*f '*(*x*) =*x*^{-1}?*f*(

*x*) =

*x*

^{-2}

*f*(

*x*) = ln

*x*

*f*(

*x*) = log

*x*

Q. Let

*f*(*x*) = cos(*x*). Then*f '*(

*x*) = sin(

*x*)

*f '*(

*x*) = cos(

*x*)

*f '*(

*x*) = -sin(

*x*)

*f '*(

*x*) = -cos(

*x*)

Q. Which function's derivative is

*f '*(*x*) = sin(*x*)?*f*(

*x*) = sin(

*x*)

*f*(

*x*) = cos(

*x*)

*f*(

*x*) = -sin(

*x*)

*f*(

*x*) = -cos(

*x*)

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