Question

differentiate following wrt x ​

Answer 1

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Answer 2

Step-by-step explanation:

${x}^{y} = {y}^{x} \\ taking \: log \: both \: sides \: \\ y log(x) = x log(y) \\ on \: differentiating \: w.r.t.x \\ y( \frac{1}{x} ) + log(x) \frac{dy}{dx} = log(y) +x \frac{1}{y} \frac{dy}{dx} \\ \frac{dy}{dx} ( log(x) - \frac{x}{y} ) = log(y) - \frac{y}{x} \\ \frac{dy}{dx} = log(y) - \frac{y}{x} \times \frac{1}{ log(x) - \frac{x}{y} }$