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Calculus - Derivatives, Tangents and Rate of Change

All solutions must be detailed and the final answers simplified. Show all work!
1. Differentiate the given function. Simplify your answer.

2. Differentiate the given function. Simplify your answer.

3. Differentiate the given function. Simplify your answer.

4. Find the equation of the line that is tangent to the graph of the given function at the specified point.

5. REFRIGERATION. An ice block used for refrigeration is modeled as a cube of side s. The block currently has volume of 125,000 cm3, and is melting at the rate of 1,000 cm3 per hour.
a. What is the current length s of the cube. At what rate is s currently changing with respect to time t ?
6. SPEED OF A LIZARD Herpetologists have proposed using the formula to estimate the maximum sprinting speed s (meters per second) of a lizard of mass w (grams). At what rate is the maximum sprinting speed of an 11-gram lizard increasing if the lizard is growing at the rate of 0.02 grams per day.

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