Math Is Fun Forum

tulip007

Member

Registered: 2008-04-30

Posts: 10

Partial derivatives are giving me nightmares!

I have a question about using the quotient rule to parial differentiate.  I seem to be confusing myself on how to get the answer and I can't get it.  Normally quotient rule is really easy for me, now I am going nuts.  If anyone could please show me how to work out this example so I can use the technique to work out other problems I would greatly appreciate it!

f(x,y) = (x + y)/(xy - 1)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Partial derivatives are giving me nightmares!

Just treat one of the variables as a constant, and differentiate with respect to the other.  If you have to, replace it with some number that won't appear anywhere else, just as pi.

df/dx is:

We have on the top (xy-1) * d(x+y).  Since y is a constant, it's derivative is 0 which just gives us the 1.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."