From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
© 2016 Shmoop University, Inc. All rights reserved.
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!
Q. Let h( x) = e 3. Which is the best choice for the inside function? x + 7
( 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
Q. If s = 4 t 2 + 3 and r = cos s, then to find the derivative of r with respect to t we would use the version of the chain rule that says
Q. The derivative of ln(5 x 6 + 7 x 2) is
Q. 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 = 0
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