Derivatives

Practice Questions

AP Calculus AB › Derivatives

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1

$\begin{align*}&\text{Approximate a forward derivative at }x=4\&\text{Using the following table:}\&x&&f(x)\&1&&5\&4&&-8\&7&&15\end{align*}$

2

Find f'(x) for the following f(x).

$f(x)=2\cdot sin(x)\cdot e^{x}$

3

Find the derivative of the function

$f=\frac{e^x}{\cos{x}}$

4

$\begin{align*}&\text{The position of a particle at a given time is given by the function:}\&p(t)=6t - sin(\frac{(5\cdot \pi t)}{2}) + 5\&\text{What is its velocity at time }t=6\text{?}\end{align*}$

5

Find the area of the region enclosed by the parabola $y=12-x^2$ and $y=-x$ .

6

A right triangle has sides of lenght and which are both increasing in length over time such that:

a) Find the rate at which the angle $\theta$ opposite is changing with respect to time.

7

Find the derivative of .

8

Find the derivative of the function:

9

Give the equation of the line tangent to the graph of the equation

$f(x) = 4x+ e^{x-2}$

at the point .

10

Given the relation , find $\frac{dy}{dx}$ .

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