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}))

Take the constant out:

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

= - \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{d}{d x} (sin (x^{2} - x))

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

y = (1 + 3 x)^{8}, (0, 1)

\int (x^{2} e^{2 x}) d x

x \to - \infty lim (f (x))

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}