How to solve this question?

Consider a function of three variables, such as F(x, y, 2) = C. Suppose , y and z are functions of t. The chain rule states that dF zple hip He p de xp dA= dt dt ar dt dy dt dz dt Of special importance are those functions where z is a function of the other variables, such as z = 5xy + 4x +2. If we know ax = cos(t) and y = sin(t), then z must be function of t too. We can find the derivative - by first rewriting our equation in the form F(x, y, 2) = -2. Then take the derivative of both sides with respect to t. The derivative of the right hand side is 0 The derivative of the left hand side requires the chain rule. First, we compute the normal: OF VF = OF ay OF where, as a function of x and y. OF 5y+4 OF 5x ay OF azThen we compute the velocity: dx dt dx = dy dt dt dz dt where as a function of t: dx -sint dt dy cost dt The value of dz can be determined because it is the only unknown quantity in the equation dt dF - 0. dt So the answer can be expressed as a function of t: dz X dt