Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.5 Exercises - Page 363: 70

$y=x$

Let $\log x$ denote the natural logarithm $\ln x$. $y=x^{\frac{1}{x}}$ $(1,1)$ $y’=(x^{\frac{1}{x}})(\frac{d}{dx}(\log x)(\frac{1}{x})$ $u=\log x$ $u’= \frac{1}{x}$ $v=x$ $v’=1$ $y’=(x^{\frac{1}{x}})(1+\log x)$ $y’(1)=1(1+\log 1)$ $=0$ Equation of Tangent: $y-1=1(x-1)$ $y=x-1+1$ $y=x$