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

The derivative of arctan(x/y) is (y-x\frac{dy)/(dx)}{x^2+y^2}

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

The first derivative of arctan(x/y) is (y-x\frac{dy)/(dx)}{x^2+y^2}

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

- \frac{1}{4} d v = v^{2} d x

\frac{20}{s ( s ^{2} + 6 s + 144 )}

y = \frac{3}{x}, y = \frac{3}{x ^{2}}, x = 4

\frac{d}{d x} (e^{t a n (2 x)})

\frac{d}{d x} (\frac{2 x - 5}{3 x - 1})

What is the derivative of arctan(x/y) ?
The derivative of arctan(x/y) is (y-x\frac{dy)/(dx)}{x^2+y^2}
What is the first derivative of arctan(x/y) ?
The first derivative of arctan(x/y) is (y-x\frac{dy)/(dx)}{x^2+y^2}