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{x ^{2}}{e ^{x}}

\int_{0}^{1} e^{- 4 x} d x

\frac{d}{d x} (C e^{- 2 x})

\int 3^{s i n (x)} cos (x) d x

P^{^{'}} = k P

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}