problem

Find the derivative of the given function.

f(x) =9^xe^4x

^and

Give your answer accurate to 3 decimal places.

Claire starts at point A and runs east at a rate of11ft/sec. One minute later, Anna starts at A and runs north at a rate of8ft/sec.At what rate (in feet per second) is the distance between them changing after another minute?

and

Give your answer accurate to 3 decimal places.

A man on a dock is pulling in a boat by means of a rope attached to the bow of the boat at a point that is1 ftabove water level. The rope goes from the bow of the boat to a pulley located at the edge of the dock7ftabove water level. If he pulls in the rope at a rate of2ft/sec,how fast (in feet per second) is the boat approaching the dock when the point of attachment is15ftfrom the dock?

ft/sec

and

Give your answer accurate to the nearest whole number.

As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at the rate of7in/min,find the rate (in cubic inches per minute) at which the sand is leaking out when the height is10in.

in³/min