What is implicit x^2=(4x+y)/(4x-y) ?

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

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implicit x^2=(4x+y)/(4x-y)

implicit derivative

x^{2} = \frac{4 x + y}{4 x - y}

\frac{d y}{d x} = \frac{x ( 4 x - y ) ^{2} + 4 y}{4 x}

Solution steps

x^{2} = \frac{4 x + y}{4 x - y}

Treat

y

y (x)

Differentiate both sides:

2 x = \frac{8 x \frac{d y}{d x} - 8 y}{( 4 x - y ) ^{2}}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{x ( 4 x - y ) ^{2} + 4 y}{4 x}

\frac{d y}{d x} = \frac{x ( 4 x - y ) ^{2} + 4 y}{4 x}

\int \frac{2 x}{4 - x ^{4}} d x

\int \frac{x + 4}{x ^{3}} d x

f (x) = 2 x - 1

\int (4 x^{7} - 3 cos (x)) d x

f (x) = 4 x + 8

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