At what rate is the water level rising when the level is 5

Question

1. Find the derivative of the function.

a) sin(x cosx)

b) y = ln(x + √(x²-1))

c) y = [x+(x+sin²x)³]⁴

d) f(x) = log₂(e^-x cosπx)

e) y = e^ktan√x

2. Use logarithmic differentiation to find the derivative of y = √(x-1/x⁴+1).

3. Water pours into a conical tank (an inverted cone) of height 10 m and radius 4 m at a rate of 6m³/min.

a. At what rate is the water level rising when the level is 5 m high?

b. As time passes, what happens to the rate at which the water level rises?