Implicit Differentiation: HELP

Question

I have no idea on how to even begin this problem:( any help would be much appreciated!

Assume that x and y are both differential equations functions of t. Find   when x = 8 and     for the equation   .

Answer 1

Let's solve first the value of y. Since x = 8 and xy =56 then 8y =56

Therefore y=7.

Remember the product rule for differentiation? Use this to get the derivative of both sides of the equation xy=56 with respect to t.

d(xy) / dt = x (dy/dt) + y (dx/dt)

d(56) /dt = 0

Therefore:

x (dy/dt) + y (dx/dt) = 0

Plug in all the given values and the value of y = 7.

8 (-9)+ 7(dx/dt) = 0

-72 + 7(dx/dt) = 0

7(dx/dt) = 72

dx/dt = 72/7