MAT125

1.Find the derivative of the function.

y = cos(cos(cos x))

2.Find an equation of the tangent line to the curve at the given point.

y = sec x,    (π/3, 2)

3.Find the derivative of the function.

y = (tan−1(2x))2

4. Differentiate the function.

f(x) = sin(5 ln x)

5. Differentiate the function.

f(x) = sin(x) ln(9x)

6.Use logarithmic differentiation to find the derivative of the function.

y = (cos 2x)x

7. The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm? Evaluate your answer numerically. (Round the answer to the nearest whole number.)

8. A plane flying horizontally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station. (Round your answer to the nearest whole number.)

9.A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 27 ft/s.

(a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.)   (b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.)  

10.Water is leaking out of an inverted conical tank at a rate of 6,500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. (Round your answer to the nearest integer.)