partial derivatives: (x,y) = x^2+ 2xy^2 + 2y/3x

[crunch]

Hi,
I'm a bit confused on how to do partial derivatives. I just started to learn it. I was doing an example word problem from the textbook.

The question: The partial derivaties f(subscript y) if (x,y) = x^2+ 2xy^2 + 2y/3x
So what I did was hold x constant. This is what I did:
= x^2 + 2xy^2 + 2y/3 (x^-1)
=x^2 + 2x2y + 2/3 (x^-1)
=X^2 +2x2y + 2/3x

but the book's answer was: 4xy + 2/3x, they made x^2= 0..why's that? I thought you would just keep it the same since you are holding it constant.

Thanks for the help in advance

 

[skeeter]

Re: partial derivatives

Hi,
I'm a bit confused on how to do partial derivatives. I just started to learn it. I was doing an example word problem from the textbook.

The question: The partial derivaties f(subscript y) if (x,y) = x^2+ 2xy^2 + 2y/3x
So what I did was hold x constant. This is what I did:
= x^2 + 2xy^2 + 2y/3 (x^-1)
=x^2 + 2x2y + 2/3 (x^-1)
=X^2 +2x2y + 2/3x

but the book's answer was: 4xy + 2/3x, they made x^2= 0..why's that?
treating x[sup:tv7ygl3p]2[/sup:tv7ygl3p] as a constant, what is its derivative?
I thought you would just keep it the same since you are holding it constant.

Thanks for the help in advance

 

[crunch]

Re: partial derivatives

ohhh ok.. I get that now.
But what confused me was because I was doing these type of questions,

ie. f(s,t) = 3t/2s = (3/2)t(s^-1)
holding t constant, I just thought you brought down the number with t,
like: (3t/2) and then find the derivative of s^-1 which is -s^-2
and then I got the same answer as the book: -3t/2s^2

am I doing that wrong or..? Im not sure what you do when you hold a variable constant, does it mean to keep it a constant? or let it be a constant?..if that made any sense...=S

 

[skeeter]

Re: partial derivatives

ohhh ok.. I get that now.
But what confused me was because I was doing these type of questions,

ie. f(s,t) = 3t/2s = (3/2)t(s^-1)
holding t constant, I just thought you brought down the number with t,
like: (3t/2) and then find the derivative of s^-1 which is -s^-2
and then I got the same answer as the book: -3t/2s^2

am I doing that wrong or..? Im not sure what you do when you hold a variable constant, does it mean to keep it a constant? or let it be a constant?..if that made any sense...=S

treat it as a constant

for f(s,t) = 3t/(2s) taking the partial with respect to s ...

f = (3t/2)s[sup:2nnxx0f8]-1[/sup:2nnxx0f8]

f'[sub:2nnxx0f8]s[/sub:2nnxx0f8] = -(3t/2)s[sup:2nnxx0f8]-2[/sup:2nnxx0f8] = -3t/(2s[sup:2nnxx0f8]2[/sup:2nnxx0f8])