What is derivative of x^4+y^4=x^2y^2 ?

The answer to derivative of x^4+y^4=x^2y^2 is (dy)/(dx)=(x(y^2-2x^2))/(y(2y^2-x^2))

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derivative of x^4+y^4=x^2y^2

derivative of

x^{4} + y^{4} = x^{2} y^{2}

\frac{d y}{d x} = \frac{x ( y ^{2} - 2 x ^{2} )}{y ( 2 y ^{2} - x ^{2} )}

Solution steps

x^{4} + y^{4} = x^{2} y^{2}

Treat

y

y (x)

Differentiate both sides:

4 x^{3} + 4 y^{3} \frac{d y}{d x} = 2 x y^{2} + 2 y \frac{d y}{d x} x^{2}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{x ( y ^{2} - 2 x ^{2} )}{y ( 2 y ^{2} - x ^{2} )}

\frac{d y}{d x} = \frac{x ( y ^{2} - 2 x ^{2} )}{y ( 2 y ^{2} - x ^{2} )}

x^{y} = y^{2}

y^{2} = - 4 x + 3

x^{5} + y^{4} = 500

s = \frac{1}{t}

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

What is derivative of x^4+y^4=x^2y^2 ?
The answer to derivative of x^4+y^4=x^2y^2 is (dy)/(dx)=(x(y^2-2x^2))/(y(2y^2-x^2))