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Please help, thanks! Consider x^2y−y^3=6.

+1 vote

Compute dy/dx.?

asked Feb 11, 2013 in CALCULUS by johnkelly Apprentice

1 Answer

+1 vote

x2y - y3 = 6

Apply 'derivative with respect to x ' each side.

(d/dx)(x2y - y3) = (d/dx)6

(d/dx)(x2y) - (d/dx)(y3) = (d/dx)6

Derivative formulas: (d/dx)constant = 0, (d/dx)(xn) = nxn-1, and (UV)'=U'V + UV'

y(2x) + x2y' - 3y2y' = 0

Subtract 2xy from each side.

x2y' - 3y2y' = - 2xy

Take out common term y'.

y'(x2 - 3y2) = - 2xy.

Divide each side by (x2 - 3y2).

So, y' = (-2xy)/(x2 - 3y2)

Therefore dy/dx = (-2xy) / (x2 - 3y2).

answered Feb 11, 2013 by richardson Scholar

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