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find dy/dx y^x + x^y+ x^x=a^b

$y^{x} + x^{y} + x^{x} = a^{b} t a k i n g \log o n b o t h s i d e s, w e g e t, \log (y^{x} + x^{y} + x^{x}) = \log a^{b} \log y^{x} + \log x^{y} + \log x^{x} = \log a^{b} x \log y + y \log x + x \log x = b \log a d i f f e r e n t i a t i n g b o t h s i d e s w . r . t . x, w e g e t, x . \frac{1}{y} . \frac{d y}{d x} + y . \frac{1}{x} + x . \frac{1}{x} = 0 \frac{x}{y} . \frac{d y}{d x} + \frac{y}{x} + 1 = 0 \frac{x}{y} . \frac{d y}{d x} = - (\frac{y}{x} + 1) \frac{x}{y} . \frac{d y}{d x} = - (\frac{y + x}{x}) \frac{d y}{d x} = - (\frac{y + x}{x}) * \frac{y}{x} \frac{d y}{d x} = - (\frac{y^{2} + y x}{x^{2}})$

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