1.

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

Answer»

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.


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