Higher Order Derivatives

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

Given the position function of f(x) = -12t²+36t+100. Find the acceleration of the object.

• -12

• -24

• -36

• -24t

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

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t

What is the acceleration of the object at time t = 2 s?

• 64 m/s/s

• 60 m/s/s

• 66 m/s/s

• 70 m/s/s

Find the second derivative of the following functions with respect to x.
y=(x³+x)/x²

• x+(1/x)
• 1-(1/x²)
• 2/x²
• 2/x³

FInd the derivative:
f(x) = (-2/3)x³ - (1/2)x² + 9x

• -2x² - x + 9
• -2x² + x + 9
• 2x² - x + 9
• 2x² - x - 9

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

• 38 m/s/s
• 27 m/s/s
• 16 m/s/s
• 49 m/s/s

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle? 

• v(t) = -2
• v(t) = -2t - 1 
• v(t) = t³
• v(t) = -t