Solve the following:
Q1. Differentiate the given function y=2 4√x3
Q2. Differentiate the given function
y=3x^5-4x^3+9x-6
Q3. Differentiate the given function
y=3/x - 2/x2 +2/3x3
Q4. Find the equation of the line that is tangent to the graph of the given function at the specified point.
y=x^5-3x^3-5x+2;(1,-5)
Q5. 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 ?
Q6. SPEED OF A LIZARD Herpetologists have proposed using the formula s=1.1w^0.2to 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.