Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Implicit partial derivatives - am I doing it right?

Here's the question:

Find

\frac{\partial f}{\partial x})_y

for

f(x,y)=\frac{x^2u+1}{axy}

, assuming that there are no implicit functions of the given variables.

Using the quotient rule:

u=x^2u+1 \rightarrow \frac{\partial u}{\partial x}=2xu+x^2\frac{\partial u}{\partial x}

v=axy \rightarrow \frac{\partial v}{\partial x}=\frac{\partial a}{\partial x}xy+ay

\frac{\partial f}{\partial x}=\frac{axy(2xu+x^2 \frac{\partial u}{\partial x})-y(x^2u+1)(\frac{\partial a}{\partial x}x+a)}{a^2x^2y^2}

(I know the above working is a bit confusing because I used the u in the quotient rule as well as it being a variable but I hope it's clear what I did.)

I just wanted to see if this is right to make sure I actually know what I'm doing... thanks!

(edited 8 years ago)

Your working seems OK to me. Have you covered the multivariable chain rule yet? That is

\frac{\partial f}{\partial u} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial u} + \frac{\partial f}{\partial y}\frac{\partial y}{\partial u}

. Questions on this topic involving the chain rule are more common (and make things a little more complicated), so I'd practice those too. :smile:

:smile:

(edited 8 years ago)

Original post by A Slice of Pi

Your working seems OK to me. Have you covered the multivariable chain rule yet? Questions involving chain rule are more common, so I'd practice those too. :smile:

:smile:

http://www.thestudentroom.co.uk/showthread.php?t=3683635

Original post by TeeEm

http://www.thestudentroom.co.uk/showthread.php?t=3683635

That looks an interesting question. I'll be sure to have a go at that later...

Original post by A Slice of Pi

That looks an interesting question. I'll be sure to have a go at that later...

https://www0.maths.ox.ac.uk/system/files/coursematerial/2015/2634/23/Prelims_Calculus_Sheet_3.pdf

Original post by Gome44

https://www0.maths.ox.ac.uk/system/files/coursematerial/2015/2634/23/Prelims_Calculus_Sheet_3.pdf

can you please post 1 and 2 and feel free to post anything else ...
in fact give us the password!

Original post by TeeEm

can you please post 1 and 2 and feel free to post anything else ...
in fact give us the password!

They're all here https://www0.maths.ox.ac.uk/courses/material :smile:

:smile:

, you don't need a password or anything to access it

Original post by Gome44

They're all here https://www0.maths.ox.ac.uk/courses/material :smile:

:smile:

, you don't need a password or anything to access it

amazing!!!
undergrad material is usually hard to find

Original post by TeeEm

amazing!!!
undergrad material is usually hard to find

There are some cambridge sheets here as well http://www.damtp.cam.ac.uk/user/examples/, but they are only for certain modules

Original post by Gome44

There are some cambridge sheets here as well http://www.damtp.cam.ac.uk/user/examples/, but they are only for certain modules

thanks

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you

The Student Room Group Privacy Notice

What is an LLM and how could it benefit your career?

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like

Why I chose a law degree and what studying law was like