Posted by: syal November 26, 2009
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Evaluate dy/dt for the function at the point.
x3 + y3 = 9; dx/dt = -3, x = 1, y = 2
x3 + y3 = 9; dx/dt = -3, x = 1, y = 2
Differentiating with respect to t on both sides;
d(x^3 + y^3)/dt = d(9)/dt
dx^3/dt + d y^3/dt = 0
Applying chain rule;
(dx^3/dx)*(dx/dt) + (dy^3/dy)*(dy/dt) =0;
(3x^2)* (-3) + (3y^2)*(dy/dt) = 0
(3*1) * (-3) + (3* 4) * (dy/dt) = 0
-9 + 12 * (dy/dt) = 0
12(dy/dt) = 9
dy/dt =9/12 = 3/4
I hope it helps.... ("^' means "to the power")