Partial Differentiation

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May 28th 2010, 08:47 AM
wkn0524

Partial Differentiation

Find : ∂z/∂x
$ z = 3x\sqrt{y} - xcos(xy) $

My solution:
$Let K = xcos(xy)$
$Let u = x , v = cos(xy)$
∂u/∂x = 1
∂v/∂x = $-ysin(xy)$
Product rule:
∂K/∂x = v(∂u/∂x) + u(∂v/∂x) = $cos(xy) - xysin(xy)$

∂z/∂x = $3\sqrt{y} -cos(xy) -xysin(xy) $
May 28th 2010, 08:55 AM
General

There is no need to make substitutions ..
Fix your function please,,
May 28th 2010, 08:59 AM
wkn0524

Sorry, im learning how to using Math equation...my final answer is ∂z/∂x = $3\sqrt{y} -cos(xy) -xysin(xy)$ . Im just want to ask whether im correct or not.
May 28th 2010, 09:05 AM
General

To write the square root of y : \sqrt{y}
You need the product rule to differentiate the second term,,
May 28th 2010, 09:12 AM
wkn0524

Quote:

Originally Posted by General

To write the square root of y : \sqrt{y}
You need the product rule to differetiate the second term,,

Thanks. What you mean by "the product rule to differetiate the second term". (Worried)
May 28th 2010, 09:15 AM
General

Quote:

Originally Posted by wkn0524

$ z = 3x\sqrt{y} - { \color{red} xcos(xy) } $

How can you differentiate the red one ?
May 28th 2010, 09:18 AM
wkn0524

Quote:

Originally Posted by General

How can you differentiate the red one ?

Sorry...The question is ask to find ∂z/∂x for this question $ z = 3x\sqrt{y} - xcos(xy) $

After differentiate xcos(xy), then i get $ cos(xy) - xysin(xy) $
May 28th 2010, 09:19 AM
General

I know,
You have:
$z=3x\sqrt{y} - x \, cos(xy)$

And you want to find $z_x$ , Right ?
May 28th 2010, 09:26 AM
wkn0524

Quote:

Originally Posted by General

I know,
You have:
$z=3x\sqrt{y} - x \, cos(xy)$

And you want to find $z_x$ , Right ?

Is ∂z/∂x = $z_x$ ?

If same, then yes.
May 28th 2010, 09:31 AM
General

Yes.
They are the same.

$z=3x\sqrt{y} - x \, cos(xy)$

$z_x=3\sqrt{y} - \left[ { \color{blue} cos(xy) - xy sin(xy) } \right]$

I used the product in blue,,
May 28th 2010, 09:36 AM
wkn0524

Quote:

Originally Posted by General

Yes.
They are the same.

$z=3x\sqrt{y} - x \, cos(xy)$

$z_x=3\sqrt{y} - \left[ { \color{blue} cos(xy) - xy sin(xy) } \right]$

I used the product in blue,,

Ouch, got the minus sign. The partial differentiation was not exactly same as differentiation topic, knew the concepts now. (Itwasntme)