A 13-foot ladder leans against a wall if the foot of the

Question

MATH 16A QUIZ 5-

(1) Let S be the set of points (x, y) in the plane that satisfy the equation (x² + y²)² = 9(x² - y²). Find the slope of the tangent line to S at (√5, 1).

(2) A 13-foot ladder leans against a wall. If the foot of the ladder is being pulled along the ground (away from the wall) at the rate of 4 feet per second, how fast is the top end of the ladder sliding down the wall at the moment the foot of the ladder is 5 feet from the wall?

(3) Find f'(0) where f(x) = ln((x + 2)²e^{x^2-5x-4}).