Answer to Question #222163 in Macroeconomics for Joe

Question

Compute the first and second order derivatives of the following:
1. Y = lnx + 3x – 2
2. Y = x

Answer 1

$y=lnx+3x-2$

First derivative

$y'=\frac {d}{dx}[lnx+3x-2]$

$y'=\frac {d}{dx}[lnx]+3\frac{d}{dx}[x]+\frac{d}{dx}[-2]]$

$y'=\frac {1}{x}+3(1)+0$

$y'=\frac {1}{x}+3$ $....................1st$

Second derivative

$y''=\frac{d}{dx}[\frac {1}{x}+3]$

$y'=-\frac {1}{x^2}$ $....................2nd$

Then for

$y=x$

$y'=\frac{d}{dx}[x]=1$ ........1st derivative

$y''=\frac{d}{dx}[1]= 0$ .........2nd derivative