What is implicit (dy)/(dx),3(x^2+y^2)^2=100xy ?

The answer to implicit (dy)/(dx),3(x^2+y^2)^2=100xy is (dy)/(dx)=(25y-3x^3-3xy^2)/(3y^3-25x+3x^2y)

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implicit (dy)/(dx),3(x^2+y^2)^2=100xy

implicit derivative

\frac{d y}{d x}, 3 (x^{2} + y^{2})^{2} = 100 x y

\frac{d y}{d x} = \frac{25 y - 3 x ^{3} - 3 x y ^{2}}{3 y ^{3} - 25 x + 3 x ^{2} y}

Solution steps

3 (x^{2} + y^{2})^{2} = 100 x y

Treat

y

y (x)

Differentiate both sides:

6 (x^{2} + y^{2}) (2 x + 2 y \frac{d y}{d x}) = 100 (y + x \frac{d y}{d x})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{25 y - 3 x ^{3} - 3 x y ^{2}}{3 y ^{3} - 25 x + 3 x ^{2} y}

\frac{d y}{d x} = \frac{25 y - 3 x ^{3} - 3 x y ^{2}}{3 y ^{3} - 25 x + 3 x ^{2} y}

\frac{d}{d x} (\frac{a ^{2} x}{( x + b ) ^{2}})

\int (6 x^{3}) d x

f (x) = \frac{cos ( x )}{cos ( x ) + 1}

y = \frac{6 x}{x ^{2} + 1}

What is implicit (dy)/(dx),3(x^2+y^2)^2=100xy ?
The answer to implicit (dy)/(dx),3(x^2+y^2)^2=100xy is (dy)/(dx)=(25y-3x^3-3xy^2)/(3y^3-25x+3x^2y)