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

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{s}{( s - 2 ) ^{2} + 16}

\frac{d}{d x} (f (x) (x)^{2} (x))

\int_{\frac{1}{3}}^{5} 16 x ln (3 x) d x

f (x) = x^{2} + 4 x - 5, at x = 2

\frac{d}{d x} (n ln (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)