Question

Solve the problem.

Determine dy/dt for x^3 + y^3 = 9 given x = 1, y = 2, and dx/dt= -3

Answer 1

Differentiate both sides with respect to
`t`, treating both
`x` and
`y` as functions of
`t`.

`x^3 + y^3 = 9 \implies 3x^2 (dx)/(dt) + 3y^2 (dy)/(dt) = 0`

Then when
`x=1`,
`y=2` and
`(dx)/(dt)=-3`, we get

`3*1^2*(-3) + 3*2^2(dy)/(dt) = 0 \implies (dy)/(dt) = \frac9{12} = \boxed{\frac34}`