# Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises - Page 453: 54

The equation of tangent at (0, 1) is $y=e$.

#### Work Step by Step

The slope of the tangent can be calculated by taking first derivative of the function $y=\frac{e^{x}}{x}$ $y'=\frac{xe^{x}-e^{x}}{x^{2}}=\frac{e^{x}(x-1)}{x^{2}}$ Slope of the tangent at $(1,e)$ is given as follows: $y'|_{(1,e)}=0$ The equation of tangent at (0, 1) is $(y-y_{1})=m(x-x_{1})$ Here $m=0$ $(y-e)=0(x-1)$ Hence, $y=e$

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