AP Calculus AB Unit 2 — Differentiation ‒ Definition and Basic Derivative Rules Practice Test

Find if the function is given by .

Find the derivative of the following function at the point x=3 . f ( x )=4 x³ + x+3

If p(t) gives the position of an asteroid as a function of time, find the function which models the velocity of the asteroid as a function of time. p ( t )=− 365 sin ( t ) +12 t³ −3 t² + 164

The function f ( x ) is differentiable at the point ( a , f ( a ) ) List which of the following statements must be true about f ( x ) :

Find the derivative of the function, y=x² sin ( 3 x ) .

What is the derivative of y=3 secθ , with respect to θ ?

Which of the following is false given the following function?  y=f ( x ) =tan x

Let g ( x ) = x^-10 ,g'(1)

Devin tried to find the derivative of Here is his work: −3 x − 11 using basic differentiation rules. At which step did Devin make a mistake, if at all?

The following table lists the value of functions g and h , and of their derivatives, g ‘ and h ‘ , for x=2

Evaluate at .

Let . Find .

Which of the following is an equation of the line tangent to the graph of h ( x )=x ⁴ −2 x² +2 x at the point where x=1

Let Find