Math 125 Test 2 7 points each (6 pts free) Feb 16, 2006

Differentiate, (means find y’(x).

1. y = sin 3x

2. y = csc (x/4)

3.

4. y = tan √x

5.

6. y = x² sin x

7.

8. y = sin² (x²)

9. y = cos 3x sin 2x

10.

11. Find y ‘(x) = dy/dx if x³ - xy + y³ = 4

12. Find the equation of the tangent line to x^1/2 + y^1/2 = 4 at the point ( 9 , 1 ).

13.. Related Rate Problem: There are 10 steps. Each step is worth 1 point.

A rock is thrown into a pond causing expanding circular rings whose radii are expanding at a rate of dr/dt = 6 m/s. How fast is the area of one of these circles increasing when its radius is 20 m?
Bonus: 10 points

1. An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 miles per hour. Find the rate at which the angle of elevation (angle above the horizontal ) of the airplane is changing when the angle is 30° .