Exam 3: Topics in Deifferentiation

Answer true or false. .

If y = (cot t)^2t, find .

Answer true or false. Water is running out of an inverted conical tank so the height is changing at a rate of 4 ft/s. The height of the water in the tank is changing at 4 ft/s if the height is currently 10 ft and the radius is 8 ft.

A conical funnel is 6 inches in diameter and 12 inches deep. A liquid is flowing out at the rate of 35 cubic inches per second. How fast is the depth of the liquid falling when the level is 8 inches deep?

Answer true or false. If y = x^{cos x},

If y = ln 6x find .

Evaluate.

Find if .

Evaluate. .

Find dy/dx if y⁷ = x⁶.

Answer true or false.

Evaluate. .

If , find the formula for $\Delta$ y.

Evaluate. .

Find f'(x) if f(x) = xln cos 3x + x⁴.

Find dy/dx by differentiating implicitly. x⁷-y⁶ = 2x

Evaluate.

A ladder 13 feet long is leaning against a wall. If the base of the ladder is moving away from the wall at the rate of 1/4 foot per second, at what rate will the top of the ladder be moving when the base of the ladder is 5 feet from the wall?

Find dy/dx by differentiating implicitly. x cos y = x⁵

Sand is falling into a conical pile so that the radius of the base of the pile is always equal to one half its altitude. If the sand is falling at the rate of 5 cubic feet per minute, how fast is the altitude of the pile increasing when the pile is 3 feet deep?