## Hoa Group Title let W(s,t) =F(u(s,t))where F,u,v are differentiable and u(1,0) =2; v(1.0)=3;us(1,0)=-2;vs(1,0)=5;ut(1,0)=6;vt(1,0)=4;Fu(2,3)=-1;Fv(2,3)=10. Find Ws(1,0) and Wt(1,0) one year ago one year ago

1. Hoa Group Title

it's quite easy to just put everything into the formula to get the answer is 34. my question is why dF/du at (1,0) can be calculate by Fu(2,3).the same problem with dF/dv

2. TuringTest Group Title

where is v in your formula?

3. Hoa Group Title

F(u(s,t),v(s,t)). where... yes. it is

4. TuringTest Group Title

W(1,0)=F(u(1,0),v(1,0))and we are told that u(1,0)=2 and v=(1,0)=3, so W(1,0)=F(2,3)

5. experimentX Group Title

looks like multivariable chain rule problem ...

6. Hoa Group Title

@experimentX yes, it is. @TuringTest and then?

7. experimentX Group Title

Fu(2,3) <--- this 2 and 3 are the values of u and v when (s,t) = (1,0) .. this is just change of variables.

8. Hoa Group Title

you mean$Ws = \frac{ \delta F }{ \delta u }\frac{ \delta u }{ \delta s }+\frac{ \delta F }{ \delta v }\frac{ \delta v }{ \delta s }$ and

9. Hoa Group Title

$\frac{ \delta F }{ \delta u }= F(2,3)$

10. Hoa Group Title

is it right?

11. TuringTest Group Title

the second formula you wrote is not right, the first is

12. experimentX Group Title

$F_u(u(1,0), v(1,0))$

13. Hoa Group Title

@TuringTest mine is wrong? why? @experimentX I think i got it. need time to make it clear in my mind. i will let you know when i get it perfectly. thanks anyway

14. experimentX Group Title

you can't simply equate the partial differential with the function itself.

15. Hoa Group Title

yes, i don't understand the goal of this part. we take partial derivative for what? tangent line respect to coordinates?

16. experimentX Group Title

$\frac{ \partial F }{ \partial u }= F_u(2,3)$ is the correct expression ... this does't have any goal. this is simply like You know a function W of 's' and 't' ... but you do not know it as an explicit function of s and t.

17. experimentX Group Title

instead you know it a function of 'u' and 'v' ... which in in turn function of 's' and 't' ... how do you find the tangent at given values of 's' and 't'?

18. Hoa Group Title

Hey. think about t is time, s is the length, and v is velocity which function respect to s,t. and we need those part to get the function of v and some u(as a variable which respect to s, t , too. I don't think we study for nothing . if putting everything in big scenario, i think we get more effect than just formula, formula...and formula

19. experimentX Group Title

suppose ... we have function like this, $\huge W(s,t) = \int_0^s \cosh (tx) dx + \sin(s)\cos(t)$ how do you calculate those partial values

20. Hoa Group Title

ok, you are right, antiderivative for those parts? we must know the technique to solve that problem, but it must be used in somewhere, right? to me, the goal of partial derivative is find out the slope of tangent line in R3 respect to x,y,z.

21. experimentX Group Title

yeah ... it is much easier to solve it (for partial) ... we can solve for it without knowing how to evaluate that integral.

22. Hoa Group Title

to x axis, the tangent line has the slope totally different from it is to y axis and z axis as well. and those tangent line has the different equation, too. and then, to each dimension in R3, each of them respect to time, to velocity of something or at least to a stable origin as earth

23. Hoa Group Title

ok, sorry, I think tooooo far. waste your time

24. experimentX Group Title

its okay ... the partial with respect to time will give you velocity along x and y axis

25. Hoa Group Title

yeah. when i were at kindergarden school, study addition and subtraction to count money or count my fingers. a little bit older, study multiplication and division to know how to count money and account. now, study partial derivative for ,,,,,don't know is really boring.

26. experimentX Group Title

i've been doing this for last 20 years

27. Hoa Group Title

and never ask yourself the silly question like me?

28. experimentX Group Title

of course i've in the past .. i think you are just little confused with the notation. while doing these sorta question .. it does smoothly unless it's hard type.

29. Hoa Group Title

Thanks for answering my question. I have many, many many homework from my classes. i wish i have 28 hours a day to solve all of them and to completely understand all of them, Thanks a lot. I have to go to school now. Hopefully I can get your help whenever I stuck at somewhere

30. experimentX Group Title

sure ... anytime!!

31. Hoa Group Title

Bye bye.