03.10 Differentiation: Composite, Implicit, and Inverse Functions Exam Part One

If dy over dx equals x times the square root of the quantity 3 minus 2 times x end quantity comma what is d squared y over dx squared question mark (10 points)

d squared y over dx squared equals 3 minus 3 times x over the square root of the quantity 3 minus 2 times x end quantity

Select which function f has an inverse g that satisfies g prime of 9 equals 1 over 9 period (10 points)

f of x equals 1 over 3 times x cubed

Let f be a decreasing function such that f(−2) = 5 and f prime of negative 2 equals 3 over 5 period Which of the following is true about its inverse h? (10 points)

h prime of 5 equals 5 over 3

If (y)sin(2y) = (x)cos(2x), then what is dy over dx at the point pi over 4 comma pi over 2 question mark (10 points)

one half

Find y ′ if y = sin−15x4. (10 points)

y prime is equal to 20 times x cubed divided by the square root of the quantity 1 minus 25 times x to the eighth power end quantity

What is the expression for the slope of the graph (x − 5)2 + (y + 1)2 = 4 at any point (x, y)? (10 points)

y prime squared equals negative quantity x minus 5 end quantity all over quantity y plus 1 end quantity

Let f be the function defined by f(x) = cot(g(x)), where g is a differentiable function. Which of the following is equivalent to the derivative of f, with respect to x? (10 points)

−csc2(g(x))g′(x)

If f ′(x) = x4 − 2x2 + 4x − 1, then what is f ‴(x) evaluated at x = 2? (10 points)

44

If y = sin(6x), then dy divided by dx is equal to which of the following? (10 points)

6cos(6x)

What is d divided by dx of inverse tangent of the quantity 2 times x squared plus 1 end quantity cubed question mark (10 points)

12 times x times the quantity 2 times x squared plus 1 end quantity squared divided by the quantity 2 times x squared plus 1 to the sixth power plus 1 end quantity