Question

xy = e^x-y
show that dy by dx = xy-y / x+xy​

Answer 1

Answer:

Step-by-step explanation:

take natural log on both sides.

=> ln(xy) = (x-y) * ln(e)

=> ln(x) + ln(y) = x-y                # log(ab) = log(a) + log(b)

Now differentiate:

the derivative of log(x) = 1/x

So we get

$\frac{1}{x} + \frac{1}{y}*\frac{dy}{dx} = 1 - \frac{dy}{dx}$

Now group both dy/dx together

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

Therefore dy/dx on simplifying will give u the ans.