Question

assume that x and y are both differentiable functions of t and find rhe required values of dy/dt and dx/dt. xy=4. find dy/dt, given x=2 and dx/dt =10

Answer 1

Differentiate both sides with respect to
`t`, using the product and chain rules on the left side.

`xy = 4 \implies x(dy)/(dt) + y (dx)/(dt) = 0`

When
`x=2`, the given equation tells us that
`2y=4\implies y=2`. Then if
`(dx)/(dt)=10`, it follows that

`2(dy)/(dt) + 2*10 = 0 \implies (dy)/(dt) = \boxed{-10}`