Step-by-step Solution

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

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Step-by-step explanation

Problem to solve:

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

Learn how to solve special products problems step by step online.

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

Unlock this full step-by-step solution!

Learn how to solve special products problems step by step online. Find the derivative of arctan((x/y)). Taking the derivative of arctangent. The derivative of a function multiplied by a constant (\frac{1}{y}) is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1. Multiplying fractions \frac{1}{1+\frac{x^2}{y^2}} \times \frac{1}{y}.

Final Answer

$\frac{y^2}{y\left(x^2+y^2\right)}$
$\frac{d}{dx}\left(arctan\left(\frac{x}{y}\right)\right)$

Main topic:

Special products

Steps:

5

Time to solve it:

~ 0.32 s (SnapXam)