Computing Derivatives: The Rules of the Game Quiz

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 h(x) = e3x + 7. Which is the best choice for the inside function?

g(x) = ex.

g(x) = 3x.

g(x) = 3x + 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 = 4t2 + 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(5x6 + 7x2) is

Q. Which function's derivative is -7sin(x)cos6 x?

cos5 x

-cos5 x

-cos7 x

cos7 x

Q. Find y' given that y is a function of x and xy + x + y = 0

Q. 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