# Step-by-step Solution

## Find the derivative of $arctan\left(\frac{y}{x}\right)$

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## Step-by-step explanation

Problem to solve:

$\frac{d}{dy}\left(arctan\left(\frac{y}{x}\right)\right)$
1

Taking the derivative of arctangent

$\frac{1}{1+\left(\frac{y}{x}\right)^2}\cdot\frac{d}{dy}\left(\frac{y}{x}\right)$
2

Applying the quotient rule which states that if $f(x)$ and $g(x)$ are functions and $h(x)$ is the function defined by ${\displaystyle h(x) = \frac{f(x)}{g(x)}}$, where ${g(x) \neq 0}$, then ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

$\frac{1}{1+\left(\frac{y}{x}\right)^2}\cdot\frac{x\frac{d}{dy}\left(y\right)-y\frac{d}{dy}\left(x\right)}{x^2}$

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$\frac{d}{dy}\left(arctan\left(\frac{y}{x}\right)\right)$

### Main topic:

Differential calculus

~ 1.23 seconds