- #1

Jonnyquest

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@f/ @x = lim h-->0 lim [f(a +h, b) - f(a, b)] / h

If possible , i'd like to seen all the calculations

Best regards

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- Thread starter Jonnyquest
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- #1

Jonnyquest

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- 0

@f/ @x = lim h-->0 lim [f(a +h, b) - f(a, b)] / h

If possible , i'd like to seen all the calculations

Best regards

- #2

CompuChip

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- #3

Fredrik

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You don't prove a definition.

- #4

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erm unless u mean the easy derivation where u start by [tex]\frac{\partial f}{\partial x}=lim_{x->a}\frac{f(x,b)-f(a,b)}{x-a}[/tex]

you can use the function [tex]g(h)=a+h[/tex]

and replace x=g(h) since [tex](lim_{x->a}x)=a=(lim_{h->0}g(h))[/tex].

you can use the function [tex]g(h)=a+h[/tex]

and replace x=g(h) since [tex](lim_{x->a}x)=a=(lim_{h->0}g(h))[/tex].

Last edited:

- #5

CompuChip

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Hello, i'm trying to proof the partial derivative definition

Ah, I missed that you are trying to prove the definition itself.

Well, that is very easy: by definition, it is true.

- #6

Jonnyquest

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But i don't how to doi it.

I already proof the simple derivative definition.

Thanks

- #7

Fredrik

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It can't be done, at least not without more information about what's considered "right".It was my Math teacher who challenged me to proof that the definition is right.

But i don't how to doi it.

Note that you

- #8

HallsofIvy

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- #9

CompuChip

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Or that is satisfies a product rule.

Or both.

Or something else entirely.

It's just guessing here what your teacher meant, so maybe you should ask him to clarify :)

- #10

Jonnyquest

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Now i've to proof that a function x^2 + y^2 is equal to 2x in order to x and by the definition ( limit ).

How do i do it ??

Thanks

Best Regards

- #11

Fredrik

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Do you know the definition of the derivative? Do you know the definition of a limit of a function? Show us your attempt to use these definitions, and we'll try to help.

I assume that what you're asking is either

"prove that if f(x)=x^{2}+y^{2}, then f'(x)=2x"

or

"prove that if "f(x,y)=x^{2}+y^{2}, then f_{,1}(x,y)=2x".

(The ",1" notation is what I use for the derivative of f with respect to the first variable). The solutions to these problems will look almost exactly the same.

I assume that what you're asking is either

"prove that if f(x)=x

or

"prove that if "f(x,y)=x

(The ",1" notation is what I use for the derivative of f with respect to the first variable). The solutions to these problems will look almost exactly the same.

Last edited:

- #12

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[tex]\frac{\partial f(x,y)}{\partial x}=lim_{h->0}\frac{(x+h)^2+y^2-(x^2+y^2}{h}=lim_{h->0}\frac{(x+h)^2-x^2}{h}=lim_{h->0}\frac{(x+h+x)(x+h-x)}{h}=[/tex]

[tex]=lim_{h->0}\frac{(2x+h)h}{h}=lim_{h->0}(2x+h)=2x.[/tex]

Now fredric is gonna be angry like his avatar image if he sees i gave u the full solution so get it fast :)...But i have to say maybe i did more harm to you than help by giving you the full solution.

- #13

Jonnyquest

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I made a small mistake , when i did the indetermination 0/0. But when i saw the solution posted by Delta , i saw the error.

Thanks to you all.

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