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Jojan
09-17-2008, 01:32 PM
I have the answer but don't know how to get to it.

I really don't understand the last step. Please try to explain it to me. You don't need to know anymore than the above to solve the problem, but I can post the full exercise if you want.

I know it's probably smarter to just send an e-mail to my docent, but this way would be more fun.

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:$\frac{\partial^2 z}{\partial s^2} = \frac{\partial}{\partial s} \left( 2 \frac{\partial z}{\partial x} + 3 \frac{\partial z}{\partial y} \right) = 4 \frac{\partial z}{\partial x} + 12 \frac{\partial z}{\partial x \partial y} + 9 \frac{\partial z}{\partial y}$

Thomas
09-17-2008, 01:39 PM
well, if I was to solve that problem, I would go about my usual method:

Stare blankly at it for a few minutes, and then either take a completely wild guess or say "fuck it", throw the paper out the window, and move out to the forest where I will live out my days surviving on berries and talking to trees.

Yeah. I got a "D" in high school trig.

T-6005
09-17-2008, 03:48 PM
The coolest part about differentiation is the name.

nameless
09-17-2008, 05:52 PM
its been years since i studied maths and even then i dont remember touching on anything like that!

Endymion
09-17-2008, 10:47 PM
you haven't posted a problem. post the whole exercise and i can help.

Jojan
09-18-2008, 10:44 AM
you haven't posted a problem. post the whole exercise and i can help.

I don't need the solution to the problem, since that's what I posted. I just want to know how to solve this step:

I know how to get left part, but not to the right part.

Endymion
09-18-2008, 10:49 AM
and i can't tell you unless i know what z or s are, or at least what they're a function of.

d/ds of (2 dz/dx + 3 dz/dy) is equal to what you'd think: 2 d^2z/dsdx + 3 d^2z/dsdy. beyond that i'd have to know what the functions are.

Jojan
09-18-2008, 11:20 PM
z = f(x,y), and I think x and y is; x = 2s-t, y = 3+2t.

Endymion
09-18-2008, 11:28 PM
edit: i think you mean y = 3x + 2t.

thus: d^2/ds^2(z) = d/ds ( dz/ds) = d/ds( dz/dx*dx/ds + dz/dy*dy/ds) (via the chain rule) = d/ds( dz/dx * 2 + dz/dy * 3)

now for the second part: d/ds(dz/dx) = d^2z/dxds = d^2z/dx^2*dx/ds + d^2z/dxdy*dy/ds and apply what dx/ds and dy/ds are again, and do the other term as well, and you end up with....

4 d^2z/dx^2 + 12 d^2z/dxdy + 9 d^2z/dy^2.

and yes, those squares are important, you shouldn't have dropped them all in what you've written out.