Question

y=x^y differentiation
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Answer 1

Answer:

$y = {x}^{y} \\ \\ take \: log \: both \: side = > \\ \\ log(y) = y log(x) \\ \\ = > \frac{1}{y} ( \frac{dy}{dx} ) = \frac{y}{x} + log(x) \frac{dy}{dx} \\ \\ = > \frac{dy}{dx} ( \frac{1}{y} - log(x) ) = \frac{y}{x} \\ \\ = > \frac{dy}{dx} = \frac{ {y}^{2} }{x(1 - y log(x)) }$