Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled

this phenomenon with the equation:

y^y = a^s ,

where a is a "magic" constant.

(a) Use implicit differentiation to find the derivative of Pinocchio's nose length with respect to his lie count. Simplify your answer. (Hint: Use the fact that y^{y =} e^{y ln y}.)

(b) Pinocchio experiences "magical balance" when his nose length equals the "magic" con- stant. If he is experiencing "magical balance" right now, what is the rate of change of his nose length with respect to his lie count when it is 6 inches long?