What is the d/(dy)(y/(x^2+y^2)) ?

The d/(dy)(y/(x^2+y^2)) is (x^2-y^2)/((x^2+y^2)^2)

What is the first d/(dy)(y/(x^2+y^2)) ?

The first d/(dy)(y/(x^2+y^2)) is (x^2-y^2)/((x^2+y^2)^2)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d y}{d y} = 1

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

= \frac{1 \cdot ( x ^{2} + y ^{2} ) - 2 yy}{( x ^{2} + y ^{2} ) ^{2}}

1 \cdot (x^{2} + y^{2}) - 2 yy = x^{2} - y^{2}

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

\int \frac{3 x ^{2}}{( x ^{3} + 1 ) ^{5}} d x

x \cdot e^{- A x}

\frac{d}{d x} (\frac{x}{( 2 x - 1 ) ^{6}})

\int (4 x + 3)^{3} d x

f (x) = e^{x^{2}} \cdot 2 x

What is the d/(dy)(y/(x^2+y^2)) ?
The d/(dy)(y/(x^2+y^2)) is (x^2-y^2)/((x^2+y^2)^2)
What is the first d/(dy)(y/(x^2+y^2)) ?
The first d/(dy)(y/(x^2+y^2)) is (x^2-y^2)/((x^2+y^2)^2)