Calc2.64

From Exampleproblems

Write $y = x^y \,$
$\Rightarrow \ln y = y \ln x \,$

$\Rightarrow \frac{y'}{y} = \frac{y}{x} + y' \ln x$

$\frac{y'}{y} - y' \ln x = \frac{y}{x}$

$y' \left [ \frac{1-y \ln x}{y} \right ] = \frac{y}{x}$

$y' = \frac{y^2}{x-xy \ln x}$

$f'(x) = \frac{ x^{2x^{x^{{\cdot}^{{\cdot}^{\cdot}}}}} }{x-x^{1+x^{x^{{\cdot}^{{\cdot}^{\cdot}}}}} \ln x } \,$