Nguyen AP Calculus Chain Rule Quiz

Find the derivative.

g(x) = sin(cos²x)

• -2cos(cos²x)sinxcosx

• -2cos(cos²x)sinx

• -cos(cos²x)sinx

• 2cos(cos²x)sinxcosx

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)
• f '(x) = x⁶ (5 + 8x)² (35 + 80x)
• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Tags

CCSS.HSA.APR.A.1

If y = f(g(x)) where y = csc³ x, choose f(x) such that we can write y = f(u)

• x
• csc x
• csc³ x
• x³

Tags

CCSS.HSF-BF.A.1C

If y = f(g(x)) where y = (6x -5)⁴, choose u such that we can write y = f(u)

• -5⁴
• 6x - 5
• (6x - 5)4
• 6x

Tags

CCSS.HSF-BF.A.1C

If y = f(g(h(x))) where y = 3 cos(tan (πx²)), choose u such that we can write y = f(g(u))

• πx²

• x²

• tan x

• tan πx²

Tags

CCSS.HSF-BF.A.1C

Find y' where y = 3 tan (πx²)

• 6xsec²(πx²)

• 3πx²sec²(πx²⁾

• 6πxsec²(πx²)

• 3sec2(πx²)

Tags

CCSS.HSF.TF.B.7

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Use the chart to find f'(3) for f(x) = g(x)/[2h(x)]

• (2π+3)/9

• -(3+2π)/9

• -(6+4π)/9

• -2(3+4π)/9

Given:  f(2)=-3, f'(2)=6, g(2)=3, g'(2)=-2, find h'(2)
for h(x) = √4g(x)-x-1  (entire expression is under the radical)

• -5/3
• -1/2
• -3/2
• -5/3

Tags

CCSS.HSF-BF.A.1B

Using the data in the chart, find the value of d/dx [g(f(x))] at x = 9

• -6+2π

• -3π

• 8+(3π)/2

• (-3π)/2