Total Differential

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Dec 18th 2011, 11:43 AM
Chipset3600

Total Differential

Find the total differential:

$u=arcsen \sqrt\frac{xz}{y}$
$du=?$

My teacher give to us this formule: $\Delta f (x,y) \approx \frac{\delta f}{\delta x} |p\Delta x + \frac{\delta f}{\delta y}|p\Delta y + \frac{\delta f}{\delta z}|p\Delta z$

but in this exercice he just dont give the point "P" and the valous of $\Delta n$
i use this formule: $\Delta f (x,y) \approx \frac{\delta f}{\delta x} + \frac{\delta f}{\delta y} + \frac{\delta f}{\delta z}$
and the result was:
part 1: http://i.imgur.com/W46hP.jpg
part 2: http://i.imgur.com/uYTek.jpg
is this correct??
Dec 18th 2011, 12:04 PM
ILikeSerena

Re: Total Differential

Hi again Chipset3600! :)

The proper formula is:

$df(x,z,y) = {\partial f \over \partial x}dx + {\partial f \over \partial y}dy + {\partial f \over \partial z}dz$

I have some trouble understanding your scans, but they do not look right.

Let's define $g(x,y,z)=\sqrt{xz \over y}$ .
And let's define $u(v)=\arcsin v$ .

What is ${\partial g \over \partial x}$ ?

And ${du \over dv}$ ?
Dec 18th 2011, 12:11 PM
Chipset3600

Re: Total Differential

dg/dx is the first derivative of G as a function of x

and du/dv is the total diferencial of function u, rite??
Dec 18th 2011, 12:16 PM
ILikeSerena

Re: Total Differential

Quote:

Originally Posted by Chipset3600

dg/dx is the first derivative of G as a function of x

Yes.
It's called the partial derivative of g as a function of x.

Quote:

Originally Posted by Chipset3600

and du/dv is the total diferencial of function u, rite??

It's just the derivative of u with respect to v.
Dec 18th 2011, 12:18 PM
Chipset3600

Re: Total Differential

well did a mistake in the formule, buts this means that my result isn's correct ? :(
Dec 18th 2011, 12:30 PM
ILikeSerena

Re: Total Differential

Well, I couldn't make sense of your first scan, so just now I skipped to the second one.

And yes! :)
Your partial derivatives are correct (except for $\partial u \over \partial y$ that should have a minus sign).

However, for the total derivative du you shouldn't have added them as you did.
Each of them should be multiplied by dx, dy, and dz respectively.
Dec 18th 2011, 12:35 PM
Chipset3600

Re: Total Differential

One more time thank you very match!
We most talk!