What is implicit (dy)/(dx),ln(x^2+y^2)=2(arctan(y/x)) ?

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

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implicit (dy)/(dx),ln(x^2+y^2)=2(arctan(y/x))

implicit derivative

\frac{d y}{d x}, ln (x^{2} + y^{2}) = 2 (arctan (\frac{y}{x}))

\frac{d y}{d x} = - \frac{x + y}{y - x}

Solution steps

ln (x^{2} + y^{2}) = 2 arctan (\frac{y}{x})

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{x + y}{y - x}

\frac{d y}{d x} = - \frac{x + y}{y - x}

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x \to 0 lim (7 sec^{2} (7 x))

\frac{\partial}{\partial x} (100 x^{0.66} y^{0.34})

\frac{d}{d x} (a^{3 x^{2}})

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