Solution assignment 02 Tangent line to graph

Calculate the slope of the tangent line at the point $P(0,0)$ of the graph of the function:

$y=xe^x$

First we calculate the derivative $y'$ of the function (using the product rule):

$y'=1.e^x+xe^x=(x+1)e^x$

In the point $(0,0)$ the derivative has the value:

$y'=(0+1)e^0=1\cdot1=1$

and thus the slope of the tangent line at $(0,0)$ equals $1$ .