Partial Derivatives

  • #1

Homework Statement


Find
∂2f
∂x2
,
∂2f
∂y2
,
∂2f
∂x∂y
, and
∂2f
∂y∂x
.
f(x, y) = 1,000 + 4x − 5y

Homework Equations




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.
 

Answers and Replies

  • #2
andrewkirk
Science Advisor
Homework Helper
Insights Author
Gold Member
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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
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
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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}##.
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
34,526
6,218

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.
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
RUber
Homework Helper
1,687
344
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.
 

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