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FadedMaster · Oct 18, 2010, 07:52 AM

Not sure why I'm blanking on this. So far I haven't been having any problems with partial derivatives. And I know the first part is probably easy, and I feel silly for tripping up on it.

Define the function

$f(x) =\left\{ {x^{4/3}sin (y/x)\mbox{ if} x\not=0 \atop 0 \mbox{ if} x = 0$

Compute

$\frac{\delta f}{\delta x} (0,1)$ and $\frac{\delta f}{\delta y} (0,1)$ using the definitions of $f_x$ and $f_y$ .

As I mentioned, I understand the method of applying the partial derivatives, but I am hung up on the definition portion.

I believe that the approach I would take is the following...

Partially differentiate with respect to x,
$\frac{\delta }{\delta x} \left[ x^{4/3} sin(\frac{y}x)\right]$

But then I must not be remembering something when finding the derivative when the function is zero... I might get it when I take a break and come back to it, but in the mean time if someone has something that can at least jog my memory, I would appreciate it.

Once I find the partial derivatives, I will have no problem calculating $\frac{\delta f}{\delta x} (0,1)$ and $\frac{\delta f}{\delta y} (0,1)$ .