Question

if y=xe^y find dy/dx​

Answer 1

Answer:

dy\dx=e^y.1+x.y.e^y.dy\dx

dy\dx(1-x.y.e^y)=e^y

dy\dx=e^y\(1-x.y.e^y)

Answer 2

Answer:

$\frac{dy}{dx} = \frac{y}{x(1 - y)}$

Step-by-step solutions:

$y = x {e}^{y} \\ = > {e}^{y} = \frac{y}{x}$

$\frac{dy}{dx} = \: \frac{d(x {e}^{y}) }{dx} \\ \frac{dy}{dx} = \: x\frac{d( {e}^{y})}{dx} \: + {e}^{y} \frac{d(x)}{dx} \\ \frac{dy}{dx} = \: x {e}^{y} \frac{dy}{dx} + {e}^{y} (1) \\ \frac{dy}{dx} \: - \frac{dy(x {e}^{y})}{dx} \: = \: {e}^{y} \\ \frac{dy(1 - x {e}^{y})}{dx} = \: {e}^{y} \\ \frac{dy(1 - y)}{dx} = \: \frac{y}{x} \\ \frac{dy}{dx} = \frac{y}{x(1 - y)}$