Question

Hello guys!
I have just started learing about derivatives and can't find in the net the answer to the following, maybe stupid, question:
Is there any difference between
d^2x/dy^2, dx^2/dy^2, d^2x/d^2y and dx^2/d^2y. If so, I would be very grateful If anyone could answer me as soon as possible. :)

Answer 1

hi
\[d^2x/dy^2=d/dy(dx/dy) = d/dy(df(x,y)/dy)\] when \[f(x,y)=x\]
all the other don't mean anything.
Hope this helps :)

Answer 2

I have finally found a good answer. For those who have the same problem as I had I will post simple explananation.

We have function x and variable y.
Derivative of this function is:
\[\frac{dx}{dy}\] or \[\frac{d}{dy}x\]
Derivative of this function is:
\[\frac{d}{dy}\frac{d}{dy}x\]
and \[dy^2 = (dy)^2\].
Then we can simplify:
\[\frac{d^2}{(dy)^2}x\] that is equal \[\frac{d^2x}{dy^2}\]

Greetings. :)

Answer 3

@ dkkmaster - be careful not to take the notation literally. d/dy is an OPERATOR - it operates on a function, changing that function into its derivative. It's not like there's some number d and some other number dy that you're dividing. Sometimes people write things like d/dy as simply D to avoid this kind of confusion.