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# Computing Derivatives

# 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*) = -3x^{-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{

*xln*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*)