Second Derivative using diff

I have a quick question concerning second derivatives using the diff function.

So, after I put in my x and y arrays I did

y1=diff(y)./diff(x)

I know that I have to change the length of y1 to take the second derivative. But I'm not sure in which order it should go. Should it be:

y1=[0 y1]

or

y1=[y1 0]

Then I would proceed to do

y2=diff(y1)./diff(x)

Any help is greatly appreciated! Thank you!

[Victor Quezada]

Hi,

I'm coming from the future (from the coronavirus-age, actually). Sorry for being late.

Try: (just a suggestion)

diff(diff(y)./diff(x))./diff(x(1:length(x)-1))

or

diff(diff(y)./diff(x))./diff(x(2:length(x)))

Ciao.

Answer 1

[Star Strider]

I wouldn’t use diff to calculate numerical derivatives. It has its uses, but I always use the gradient function for derivative calculations, since gradient produces a result the same size as its argument.

[Star Strider]

Claire’s Answer moved here...

But if I had to use diff for a certain problem, how would I go about this? (The problem specifies to use diff)

[Star Strider]

I wouldn’t zero-pad it if you’re using it to calculate a numerical derivative, and for that matter you don’t have to since both ‘diff(y)’ and ‘diff(x)’ are going to be the same lengths. You have to live with the fact that the calculation using diff is going to be shorter than the original vectors. (You would have to zero-pad both at the same location. That would create a NaN value where both were zero. So you can pad with NaN values or use interp1 with the 'extrap' option if you wanted the derivative vectors to be the same lengths as the original vectors.)

For the second derivative, just go directly to it:

x = randi(10, 1, 10);
y = randi(10, 1, 10);

d2ydx2 = diff(y,2)./diff(x,2);

Answer 2

[Sanskruti Sawant]

1/x