# Numerical differentiation problem?

• Oct 23rd 2010, 04:01 PM
chronicals
Numerical differentiation problem?
xi=[ 0.1 0.2 0.3 0.4 0.5 0.6]

yi=[1.621 1.408 1.266 1.170 1.104 1.060]

What is d ln(yi) / d ln(xi) = ?
• Oct 23rd 2010, 05:35 PM
Jhevon
Quote:

Originally Posted by chronicals
xi=[ 0.1 0.2 0.3 0.4 0.5 0.6]

yi=[1.621 1.408 1.266 1.170 1.104 1.060]

What is d ln(yi) / d ln(xi) = ?

find the log of each of the xi's and yi's. then use the slope formula to find the derivative. remember, the derivative gives the slope.
• Oct 23rd 2010, 09:01 PM
chronicals
Quote:

Originally Posted by Jhevon
find the log of each of the xi's and yi's. then use the slope formula to find the derivative. remember, the derivative gives the slope.

I write this in matlab:

>> x=0.1:0.1:0.6

x =

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000

y=[1.621 1.408 1.266 1.170 1.104 1.060];

>> k=log(y)

k =

0.4830 0.3422 0.2359 0.1570 0.0989 0.0583

>> l=log(x)

l =

-2.3026 -1.6094 -1.2040 -0.9163 -0.6931 -0.5108

and this our result:

>> z=diff(k)./diff(l)

z =

-0.2032 -0.2622 -0.2741 -0.2602 -0.2231

but in my book the result is different:

d ln(y) / d ln (x)= [ -0.246 - -0.249 - -0.2.44 -]

i must reach the book's result, but how?