Find the derivative of x/((x^2+y^2)^0.5)
Answer
$\frac{\sqrt{y^2+x^2}-x\frac{d}{dx}\left(\sqrt{y^2+x^2}\right)}{y^2+x^2}$
Step-by-step explanation
Problem
$\frac{d}{dx}\left(\frac{x}{\sqrt{x^2+y^2}}\right)$
1
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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
$\frac{\sqrt{y^2+x^2}\cdot\frac{d}{dx}\left(x\right)-x\frac{d}{dx}\left(\sqrt{y^2+x^2}\right)}{\left(\sqrt{y^2+x^2}\right)^2}$
Answer
$\frac{\sqrt{y^2+x^2}-x\frac{d}{dx}\left(\sqrt{y^2+x^2}\right)}{y^2+x^2}$