5/12 Review 2_Chain Rule, Derivatives, and Implicit Differe.

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

Find the derivative of f(x)=(x³-2x)²

• 6x⁵ - 12x³+8x
• 6x⁵ - 16x³+8x
• x⁶-4x⁴+4x²
• 6x⁵ - 16x^3-8x

• A

• B

• C

• D

find y' for y=(e^5x)+1

• 5e^5x+1

• e^5x

• 5e^5x

• 1

Tags

CCSS.HSF-IF.C.8B

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

Find the second derivative of the following functions with respect to x.
y=3x⁴

• 36x²
• 12x³
• 4x³
• 12x²

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

• 200x³+36x² -30x+4

• 600x² +72x -26

• 600x² +72x -30

• 600x² +72x -36

Tags

CCSS.HSA.APR.A.1

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?  

• v = 0
• v = 1
• v = -1
• v = -2