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# Computing Derivatives

# Computing Derivatives: The Rules of the Game 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

*h*(*x*) = e^{{3x + 7}}. Which is the best choice for the inside function?*g*(

*x*) = e

^{x}.

*g*(

*x*) = 3

*x*.

*g*(

*x*) = 3

*x*+ 7

*g*(

*x*) =

*x*.

Q. The function

*h*(*x*) is composed of two functions. The outside function is cos (□) and the inside function is*ln*x. Which formula best describes*h*?*h*(

*x*) = cos(

*ln*

*x*)

*h*(

*x*) =

*ln*(cos

*x*)

*h*(

*x*) = cos

*x*×

*ln*

*x*

*h*(

*x*) = (cos

*x*)

^{{ln x}}

Q. The chain rule says that if

*h*(*x*) =*f*(*g*(*x*)), then*h'*(

*x*) = f'(

*g'*(

*x*))

*h'*(

*x*) = f(

*g'*(

*x*))

*h'*(

*x*) = f'(

*g*(

*x*))

*g'*(

*x*)

*h'*(

*x*) = f(

*g'*(

*x*))

*f'*(

*x*)

Q. Find the derivative of the function

*f*(*x*) = (cos*x*)^{-3}.*f'*(

*x*) = -3(cos

*x*)

^{{-4}}sin

*x*

*f'*(

*x*) = 3(cos

*x*)

^{{-4}}sin

*x*

*f'*(

*x*) = -3(cos

*x*)

^{{-2}}sin

*x*

*f'*(

*x*) = 3(cos

*x*)

^{{-2}}sin

*x*

Q. Suppose

*f*and*g*are inverses so that*f*(*g*(*x*)) =*x*. Then*g'*(

*x*) = f

^{-1}(

*g*(

*x*))

Q. If

*s*= 4t^{2}+ 3 and*r*= cos*s*, then to find the derivative of*s*, then to find the derivative of*r*with respect to*t*we would use the version of the chain rule that saysQ. The derivative of

*ln*(5*x*^{6}+ 7*x*^{2}) isQ. Which function's derivative is -7sin(

*x*)cos^{6}*x*?cos

^{5}*x*-cos

^{5}*x*-cos

^{7}*x*cos

^{7}*x*Q. Find

*y'*given that*y*is a function of*x*and*xy*+*x*+*y*= 0Q. To use implicit differentiation on the equation we need to use

the chain rule and the product rule

the chain rule but not the product rule

the product rule but not the chain rule

neither the product rule nor the chain rule