Suppose that x=x(t) & y=y(t) are both functions of t. If y^2 + xy - 3x = 1, and...(see below)

dy/dt = 1 when x = 3 and y = -5, what is dx/dt?

PLEASE HELP!

... y² + xy - 3x = 1 .......... (1)

Diff... w.r.t. t, by Chain Rule,

... (2y). (dy/dt) + [ x.(dy/dt) + y.(dx/dt) ] - 3.(dx/dt) = 0

Putting x = 3, y = -5 and dy/dt = 1 in this equation,

... 2(-5)(1) + (3)(1) + (-5)(dx/dt) - 3(dx/dt) = 0

∴ -8(dx/dt) = 7

∴ dx/dt = -7/8 ................................ Ans.
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