# Thread: Equation using derivative: Use a derivative to estimate g(e+0.1) for g(x) = xln(x)

1. ## Equation using derivative: Use a derivative to estimate g(e+0.1) for g(x) = xln(x)

Let g(x)=xln(x). We know g(e)=e. Use a derivative to estimate g(e+0.1). You may leave an unsimplified numerical answer.

2. Originally Posted by tsj1114
Let g(x)=xln(x). We know g(e)=e. Use a derivative to estimate g(e+0.1). You may leave an unsimplified numerical answer. I understand how to plug g(e+0.1) in, but not using the derivative.
If $h \approx 0$ then $g'(x_0)\approx \dfrac{g(x_0+h)-g(x_0)}{h}$ then rearranging we get
$g(x_0+h)\approx h\cdot g'(x_0)+g(x_0)$.

$g(x)=x\log(x)~ \Rightarrow~g'(x)=\log(x)+1$ Thus let $x_0=e~\&~h=0.1$.