# Math Help - Implicit Differentiation

1. ## Implicit Differentiation

I have three problems. So hopefully it is okay if I post all three on one. Please help me solve one, two, or all It is from the review for my exam tomorrow.

1) In calm waters, oil spilling from the ruptured hull of a grounded tanker spreads in all directions. Assuming that the area polluted is a circle and that its radius is increasing at a rate of 2 ft/sec, determine how fast the area is increasing when the radius of the circle is 40 feet.

2) A 20-foot ladder is leaning against a wall. If the bottom of the ladder is pulled away from the wall at a rate of 2 ft/sec, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 12 feet from the wall.

3) Jane is at the top of a 5-foot ladder when it starts to slide down the wall at a rate of 3 feet per minute. Jack is standing on the ground behind her. How fast is the base of the ladder moving when it hits him if Jane is 4 feet from the ground at that instant?

Thanks everyone!!!

2. You are supposed to show some of your work. This may include a partial solution or describing your difficulty.

For 1), as you know, the area of the circle depending on time is $\pi (r(t))^2$, so you can find the derivative.