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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

0.75 400 + 0.25 900

s (s + 1) (s + 2) (s + 4)

lo g_{10} (8) - lo g_{10} (2)

2 π (5)

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