# Chapter 4 - Calculating the Derivative - Chapter Review - Review Exercises - Page 245: 62

$y = 2x - e$

#### Work Step by Step

$\begin{gathered} y = x\ln x \hfill \\ Evaluate\,\,the\,\,function\,\,at\,\,x = e \hfill \\ y = \,\left( e \right)\ln \,\left( e \right) \hfill \\ y = e\,\,,\,\,Point\,\,\left( {e,e} \right) \hfill \\ Find\,\,the\,\,deriva\,tive\,\,of\,\,the\,\,function \hfill \\ {y^,} = \,\,{\left[ {x\ln x} \right]^,} \hfill \\ {y^,} = x\,\left( {\frac{1}{x}} \right) + \ln \,\left( x \right)\,\left( 1 \right) = 1 + \ln x \hfill \\ Evaluate\,\,{y^,}\,\left( e \right) \hfill \\ {y^,} = 1 + \ln \,\left( e \right) = 2 \hfill \\ m = 2 \hfill \\ Use\,\,the\,\,point\, - slope\,\,form \hfill \\ y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\ y - e = 2\,\left( {x - e} \right) \hfill \\ y = 2x - e \hfill \\ \end{gathered}$

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