Derivative Rules - Polynomials and Exponential Functions

c is a constant.

• 0

• 1

• cx

• c²

• 
• 
• 
• 

The derivative of which function is itself?

• e^x
• x
• sinx
• tanx

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

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

• 7
• 0
• 7x
• 14

How do you rewrite this in power form:

 $f\left(t\right)=\frac{1}{t}-\frac{3}{t^2}+\frac{5}{t^3}$  

•  $f\left(t\right)=t^{-1}-3t^{-2}+5t^{-3}$  

•  $f\left(t\right)=-t^{-2}+6t^{-3}-15t^{-4}$  

•  $f\left(t\right)=-t^{-2}+t^{-3}-t^{-4}$  

•  $f\left(t\right)=\ t^{-2}-6t^{-3}+15t^{-4}$   

Find the derivative of the given equation
f(x) = 1/x²

• 1/2x
• -2x
• 2x
• -2x^-3

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

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