Question

Please help me

find dy/dx using implicit differentiation
e^((x+y)/4) +tan(ln(x/y)) = e^sqrt(y)

Answer 1

Explanation:

Taking log both sides :

`( (x + y)/(4) ) + \tan( ln( (x)/(y) ) ) = √(y)`

Differentiate both sides w.r.t x :

`(1)/(4) + (1)/(4) (dy)/(dy) + {sec}^(2) ( ln(x)/(y) ) + (y)/(x) + (1)/(y) - \frac{x}{ {y}^(2) } = (1)/(2 √(y) ) (dy)/(dx)`

Rearranging :

`( (4 - 2 √(y) )/(8 √(y) )) ((1)/(4) + {sec}^(2) ( ln(x)/(y) ) + (y)/(x) + (1)/(y) - \frac{x}{ {y}^(2) }) = (dy)/(dx)`

(You can rearrange it further)