Thread: partial derivative, help please

1. partial derivative, help please

Hi,
This is my first post so I do not know how to properly insert the partial derivative symbol, therefore “d” stands not for derivative but for partial derivative.

I have been trying to solve this exercise since Friday and I have no idea what to do:
Compute
d^(137)f / [(dx^(72))(dy^3)(dx)(dx)(dy^(60))]
for f(x,y) = cos (2x – y)
Any suggestions will help

thanks!

2. Originally Posted by alekb
Hi,
This is my first post so I do not know how to properly insert the partial derivative symbol, therefore “d” stands not for derivative but for partial derivative.

I have been trying to solve this exercise since Friday and I have no idea what to do:
Compute
d^(137)f / [(dx^(72))(dy^3)(dx)(dx)(dy^(60))]
for f(x,y) = cos (2x – y)
Any suggestions will help

thanks!
ouch! i'm assuming you mean $\frac {\partial ^{137} f}{\partial x^{72} \partial y^3 \partial x \partial x \partial y^{60}}$

Basically what this is asking you to do is differentiate $f$ with respect to $y$ 60 times, then the resulting function with respect to $x$ twice, then that resulting function with respect to $y$ three times, then finally the resulting function with respect to $x$ 72 times.

in each case, i'd just do it a few times and try to pick up a pattern of what it would look like after doing it 60 and 72 times. good luck. seems like it will be a pain, but maybe not as hard as you think. maybe.

3. Indeed, that's what I meant.

So, can I combine those partial derivatives and then multiply both results?(differentiate f with respect to y 63 times and f with respect to x 74 times), or do I need to follow the order that you posted?

Thanks!

4. Originally Posted by alekb
Indeed, that's what I meant.

So, can I combine those partial derivatives and then multiply both results?(differentiate f with respect to y 63 times and f with respect to x 74 times), or do I need to follow the order that you posted?

Thanks!
no multiplication goes on here. you just differentiate the function over and over (that is, differentiate the function, then differentiate the result, then differentiate that result, etc). and yes, it has to be in the exact order i said.