What is the d/(dy)(-arctan(x/y)) ?

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

What is the first d/(dy)(-arctan(x/y)) ?

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

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\frac{d}{d y} (- arctan (\frac{x}{y}))

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

Solution steps

\frac{d}{d y} (- arctan (\frac{x}{y}))

Treat

x

as a constant

Take the constant out:

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

= - \frac{d}{d y} (arctan (\frac{x}{y}))

Apply the chain rule:

\frac{1}{( \frac{x}{y} ) ^{2} + 1} \frac{d}{d y} (\frac{x}{y})

= \frac{1}{( \frac{x}{y} ) ^{2} + 1} \frac{d}{d y} (\frac{x}{y})

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

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

Simplify

- \frac{1}{( \frac{x}{y} ) ^{2} + 1} (- \frac{x}{y ^{2}}) : \frac{x}{x ^{2} + y ^{2}}

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

\int_{0}^{π} 9 sin^{2} (t co) s^{4} t d t

\int 6 tan^{2} (x) d x

\int x^{2} - 4 x + 8 d x

\frac{d}{d x} (lo g_{7} (x^{2} + e^{x}) - ln (ln (x)))

\frac{d}{d x} (25 - x^{2})

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