Derivatives

What is the power rule and how do you use it take a derivative of an expression like 2x^5?

Find the derivative.
 f(z) = 1/(3z²) + 4z³

• f'(z) = 6z³ + 12z²
• f'(z) = 6z + 12x²
• f'(z) =  -2/(3z³) + 12z²
• f'(z) = -6/z² + 12z²

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

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

Tags

CCSS.HSF.IF.A.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

Tags

CCSS.HSA.SSE.A.1

• A
• B
• C
• D

Tags

CCSS.HSF.IF.A.2

• A
• B
• C
• D

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2
• 3(x²+2)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

find 

• y = 2 x^-1
• y=2 x^-2
• y= −2x^-2
• y= −2 x^-1

Tags

CCSS.HSF-IF.C.7A

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1