Mid Unit 3 Review

Chain Rule

100

Find f’(x) when f(x) = (2x - 7)³

f’(x) = 6(2x - 7)²

200

Find dy/dx if y=2(-7x-2)^-3

Write your answer with no negative exponents

 

dy/dx=42/(-7x-2)^4

300

Find f’(x) when

f(x) = 3sqrt(sinx)

Write your answer with no negative exponents

 

f'(x) = (3cosx)/(2sqrt(sinx))

400

Find f’(x) when f(x) = log₃(2x + 9)

 

f'(x) = 2/((2x+9)ln3)

500

Find dy/dx when y=2sin⁴(4+x²)

dy/dx=16xsin³(4+x²)cos(4+x²)

Inverse Derivatives

100

g satisfies g(4)=6 and g'(4)=-2. What is the value of (g^-1)'(6)?

-1/2

200

f satisfies f(10)=5 and f'(10)=8. What is the value of (f^-1)'(5)?

1/8

300

The function f is defined by f(x)=-x³-4x+5 and the point (-1, 10) is on the graph of f. If g is the inverse function of f, what is the value of g'(10)?

-1/7

400

The function f is defined by f(x)=2x³+4x+2 and f(−1)=−4. If g is the inverse function of f, what is the value of g′(−4)?

1/10

500

Let f and g be inverse functions that are differentiable for all x. If f(-5)=7 and g'(7)=3, what is f'(-5)?

1/3

Higher Order Derivatives

100

Find y" if y=2x⁴-5x²+3

y"=24x²-10

200

Find f’’’(x) if f(x) = 23x⁴

f’’’(x) = 552x

300

Find f’’’’(x) if f(x) = -sinx

f’’’’(x) = -sinx

400

Find d²y/dx² if f(x) = cos(2x²) - 26x³

d²y/dx² = -4sin(2x²) - 16x²cos(2x²) - 156x

500

Find f’’’(x) if f(x) = -cos(3x) + sin(x²)

f’’’(x) = -27sin(3x) -12xsin(x²) - 8x³cos(x²)

Implicit Differentiation

100

Find dy/dx if y² - x² = 6

dy/dx = x/y

200

Find dy/dx if 2y³ + 4x² - y = x⁶

dy/dx = (6x⁵ - 8x)/(6y² - 1)

300

Find y' if 2x²+3xy²+4y³=2

y'=(-4x-3y^2)/(6xy+12y^2)

400

Find dy/dx if cos(y³) = x³ + 2x + 5

dy/dx = (3x² + 2)/(-3y²sin(y³))

500

Find dy/dx if 4y⁴ = 6cos(x³) - sin(y²)

dy/dx = (-9x²sin(x³))/(8y³ + ycos(y²))

Tangent Lines

100

Write the equation of the tangent line for f(x) = x²+1 at (5, 26)

y - 26 = 10(x - 5)

200

Write the equation of the tangent line for f(x) = 3x² + 5 at x = 2

y - 17 = 12(x - 2)

300

Write the equation of the tangent line to y = sin(2x) at x = 5π/6

y + √3/2 = (x - 5π/6)

400

Write the equation of the tangent line to y = sin²(x) at x = π/4

y - 1/2 = (x - π/4)

500

Write the equation of the tangent line to x⁴ + y² = 3 at (1, -√2)

y + √2 = 2/√2 (x - 1)