An edge of a variable cube is increasing at the rate of 5 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

Find an angle x which increases twice as fast as its sine.

The radius of a balloon is increasing at the rate of 10 m/s. At what rate is the surface area of the balloon increasing when the radius is 15 cm?

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. Find the rate at which the area is increasing when the side is 10 cm.

Using differentials, find the approximate values of: