What is the derivative of arctan(y/x) ?

The derivative of arctan(y/x) is x/(y^2+x^2)

What is the first derivative of arctan(y/x) ?

The first derivative of arctan(y/x) is x/(y^2+x^2)

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derivative of

arctan (\frac{y}{x})

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{d}{d y} (\frac{y}{x}) = \frac{1}{x}

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

Simplify

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

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

(sin (t))^{^{'}}

f (x) = 4 x^{2} - 15

e^{2 x} y^{^{'}} - 4 y = 0

\frac{d}{d x} (x^{\frac{8}{9}})

n = 1 \sum \infty \frac{x ^{n}}{4 ^{n}}

What is the derivative of arctan(y/x) ?
The derivative of arctan(y/x) is x/(y^2+x^2)
What is the first derivative of arctan(y/x) ?
The first derivative of arctan(y/x) is x/(y^2+x^2)