Exam 2: Derivatives

Differentiate.

A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to mm. The area is A(x). Find ( ).

The displacement of a particle on a vibrating string is given by the equation where s is measured in centimeter and t in seconds. Find the velocity of the particle after t seconds.

Find the derivative of the function.

s(t) is the position of a body moving along a coordinate line; s(t) is measured in feet and t in seconds, where . Find the position, velocity, and speed of the body at the indicated time. ; t = 3

Differentiate.

Calculate .

s(t) is the position of a body moving along a coordinate line, where , and s(t) is measured in feet and t in seconds. a.Determine the time(s) and the position(s) when the body is stationary. b.When is the body moving in the positive direction? In the negative direction? c.Sketch a schematic showing the position of the body at any time t.

Match the graph of the function with the graph of its derivative.

Differentiate the function.

The curve with the equation is called an astroid. Find an equation of the tangent to the curve at the point ( , 1).

Refer to the law of laminar flow. Consider a blood vessel with radius 0.01 cm, length 3 cm, pressure difference and viscosity $\eta$ =0.028. Find the velocity of the blood at radius r =

If u is a differentiable function of x and f (x) = |u| then . Use this to find the derivative of the following function. F (x) = |x² - 4|

Find

Find the instantaneous rate of change of the function when

Find the derivative of the function.

If a tank holds 5000 gallons of water, and that water can drain from the tank in 40 minutes, then Torricelli's Law gives the volume V of water remaining in the tank after t minutes as . Find the rate at which water is draining from the tank after 6 minutes.

Find the average rate of change of the area of a circle with respect to its radius r as r changes from to .

Find

Find the rate of change of y with respect to x at the given values of x and y. ; x = 3, y = -5