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use implicit differentiation to find dx/dy.

0 votes

x^4y^2 -x^3y +2xy^3=0

asked Aug 7, 2013 in CALCULUS by linda Scholar

1 Answer

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The function is x4y2 - x3y + 2xy3 = 0.

Differentiate the function with respect to y.

(x4y2) ' - (x3y) ' + (2xy3) ' = 0

Apply product rule : (uv) ' = uv ' + vu '.

x4(y2) ' + y2(x4) ' - x3(y) ' - y(x3) ' + 2x(y3) ' + 2(y3)x ' = 0

Apply power rule : (xn) ' = nxn - 1 .

x4(2y) + y2(4x3) x ' - x3(1) - y(3x2) x ' + 2x(3y2) + 2(y3)x ' = 0

2x4y + 4x3y2x ' - x3 - 3x2yx ' + 6xy2 + 2y3x ' = 0

4x3y2x ' - 3x2yx ' + 2y3x ' = x3 - 6xy2 - 2x4y

x ' = (x3 - 6xy2 - 2x4y) / (4x3y2 - 3x2y + 2y3).

Therefore, dx / dy = (x3 - 6xy2 - 2x4y) / (4x3y2 - 3x2y + 2y3).

answered Aug 9, 2014 by lilly Expert

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