Question

partial derivative: f(x,y) arctan(y/x)

Answer 1

ok we need to apply the chain rule for this partial derivative...

Answer 2

\[u=\frac{x}{y} \longrightarrow \frac{d}{du}\tan^{-1}(u)=\frac{1}{1+u^2}\]

Answer 3

\[\frac{\delta}{\delta x}\frac{\frac{x}{y}}{\frac{y^2}{x^2}+1}\]

Answer 4

\[=y \frac{\frac{\delta}{\delta x}\frac{1}{x}}{\frac{y^2}{x^2}+1}\]
\[= -\frac{y}{x^2\frac{y^2}{x^2}+x^2}\]

Answer 5

...etc

Answer 6

thanks