Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 362: 63

$y'=(2x^{\frac{2}{x}-2}(1-\ln x))$

$y=x^{\frac{2}{x}}$ $y’=(x^{\frac{2}{x}})(\frac{d}{dx} \ln x (\frac{2}{x}))$ $u= 2\ln x$ $u’= \frac{2}{x}$ $v=x$ $v’=1$ $y’=(\frac{(\frac{2}{x})(x)-(2 \ln x)(1)}{x^2})(x^{\frac{2}{x}})$ $=(2x^{\frac{2}{x}-2}(1-\ln x))$