Step-by-step explanation:
Taking log both sides :
[tex]( \frac{x + y}{4} ) + \tan( ln( \frac{x}{y} ) ) = \sqrt{y} [/tex]
Differentiate both sides w.r.t x :
[tex] \frac{1}{4} + \frac{1}{4} \frac{dy}{dy} + {sec}^{2} ( ln\frac{x}{y} ) + \frac{y}{x} + \frac{1}{y} - \frac{x}{ {y}^{2} } = \frac{1}{2 \sqrt{y} } \frac{dy}{dx} [/tex]
Rearranging :
[tex]( \frac{4 - 2 \sqrt{y} }{8 \sqrt{y} }) (\frac{1}{4} + {sec}^{2} ( ln\frac{x}{y} ) + \frac{y}{x} + \frac{1}{y} - \frac{x}{ {y}^{2} }) = \frac{dy}{dx} [/tex]
(You can rearrange it further)
