# Homework Help: How to find a general expression for derivative

1. Oct 4, 2012

### east

Hello everybody,

I am trying to solve this problem but I can't find an answer reading my book :(

Let z=F(u,w,x) where u=f(x,y) and w=g(x,y)

(i) find a general expression for Dxz
(ii) verify your answer in the case where F(u,w,x)=w3-2ux, f(x,y)=4xy-x+1 and g(x,y)=y+xy2

Many thanks

2. Oct 4, 2012

### Ray Vickson

Other than trying to find it in your book, what else have you tried? Forum rules require you to show your work.

RGV

3. Oct 4, 2012

### east

Yes, I've read the rules, sorry. the point is that I don't know where to stard with :( more than the just the solution I would like some references to books or links where I can study the problem..

thx again

4. Oct 4, 2012

### Ray Vickson

So, are you saying you have never encountered such material before? You have never heard of the chain rule?

RGV

5. Oct 4, 2012

### east

sadly no :( I have to take a test of basic math knowledge and we only have some notes to prepare... but ty for the hint of the chain rule :)

6. Oct 4, 2012

### east

ok, thx to RVG who explained me where to look for the solution I think I have solved it:

(i): Dz/Dx=DF/Du*DU/Dx+DF/Dw*DW/Dx+DF/Dx

(ii) Dz/Dx= -2x(4y-1)+3w2y2-2u

Is it right? it is fairly easy once discovered wich formula to use (if I've used the right one of course)

7. Oct 4, 2012

### Ray Vickson

Yes, you have made a correct start in part (i) and you have a correct result in part (ii) (although I guess there is an issue of whether or not to plug in the actual values of u and w and do a complete simplification).

RGV

8. Oct 4, 2012

### SammyS

Staff Emeritus
Yes, that looks good.

I used WolframAlpha to compare: