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}})

Simplify

\frac{- y}{x ^{2} + y ^{2}} : - \frac{y}{x ^{2} + y ^{2}}

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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}}

\frac{d}{d x} (lo g_{2} (3 x + 1))

x y^{^{'}} + y = x

\frac{d}{d x} (\frac{( - 5 x + 1 ) ^{3}}{( 3 x - 3 ) ^{6}})

\frac{\partial}{\partial x} (x^{2} - y^{2} - 2 z^{2})

\frac{d}{d x} (\frac{12 x ^{5} + 8 x ^{3} - 2 x ^{2}}{4 x ^{2}})

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)