Partial Derivatives

Tags:
1. Aug 30, 2015

Julian12345

1. The problem statement, all variables and given/known data
Find
∂2f
∂x2
,
∂2f
∂y2
,
∂2f
∂x∂y
, and
∂2f
∂y∂x
.
f(x, y) = 1,000 + 4x − 5y

2. Relevant equations

3. The attempt at a solution
Made somewhat of an attempt at the first one and got 0, however my teacher has poorly covered this in class, and I would value some further explanation.

2. Aug 30, 2015

andrewkirk

0 is correct for the first one, but how did you get it? Set out your working and you may be able to see how to do the others using a similar approach. If not, somebody may be able to help you move on from where you are up to.

What is your understanding of the meaning of $\frac{\partial^2f}{\partial x\partial y}$?

By the way, to write partial derivatives neatly, use latex code. The following code
\frac{\partial^2f}{\partial x^2}
when enclosed between double-# delimiters at each end, gives $\frac{\partial^2f}{\partial x^2}$.

3. Aug 30, 2015

Ray Vickson

Alternatively, you can just write $\partial^2 f/ \partial x^2$, and it should still be perfectly readable. Right-click on the displayed expression and then choose the "display math as Tex commands" menu item.

4. Aug 31, 2015

Staff: Mentor

In addition to what your teacher has covered in class, there should be some explanation in your textbook. Have you read the section that discusses partial derivatives? There should be some examples in your book. You shouldn't rely only on what the teacher does in class.

5. Aug 31, 2015

RUber

If you consider multiple derivatives as a sequence, these problems become less confusing.
$\frac{\partial ^2 f}{\partial x^2 } = \frac{\partial }{\partial x }\left( \frac{\partial }{\partial x}f\right)$
Similarly,
$\frac{\partial ^2 f}{\partial x \partial y } = \frac{\partial }{\partial x }\left( \frac{\partial }{\partial y}f\right)$.
Do the operations in order, and you will get the correct result.