Question

find dy/dx,
If e^2x+e^2y=e^2(x+y)​

Answer 1

Answer:

${e}^{2x} + {e}^{2y} = {e}^{2(x + y)} \\ \\ diff. \: \: wrt \: \: x \: and \: use \: chain \: rule \\ \\ {e}^{2x} (2)+ {e}^{2y}(2 \frac{dy}{dx} ) \\ = {e}^{2(x + y)}. \frac{d}{dx} (2(x + y)) \\ = {e}^{2(x + y)}. 2(1 + \frac{dy}{dx} ) \\ \implies \\( {e}^{2(x + y) } - { {e}^{2y}) }. \frac{dy}{dx} = {e}^{2x} - {e}^{ 2(x + y)} \\ \implies \\ \frac{dy}{dx} = \frac{{e}^{2x} - {e}^{ 2(x + y)}} { {e}^{2(x + y) } - { {e}^{2y} }} = \frac{1 - {e}^{2y} }{ {e}^{2x} - 1 }$