Can someone please explain how I would differentiate this:

(1-e^(-x^2))(1-e^(-y^2))

and integrate this:

24y(1-x-y)

Regards.

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- Nov 15th 2011, 11:23 AMWevans2303Integration/Differentiation help.
Can someone please explain how I would differentiate this:

(1-e^(-x^2))(1-e^(-y^2))

and integrate this:

24y(1-x-y)

Regards. - Nov 15th 2011, 12:09 PMTheEmptySetRe: Integration/Differentiation help.
- Nov 15th 2011, 12:10 PMWevans2303Re: Integration/Differentiation help.
Apologies TES.

Differentiating w.r.t x and a double integral dydx. - Nov 15th 2011, 12:26 PMTheEmptySetRe: Integration/Differentiation help.
So for the first question if you have

$\displaystyle f(x,y)=\dfrac{1-e^{-x^2}}{1-e^{-y^2}}$

The partial derivative with respect to x is

$\displaystyle \dfrac{\partial f}{\partial x}=\dfrac{1}{1-e^{-y^2}}\dfrac{\partial }{\partial x} (1-e^{-x^2})= \dfrac{1}{1-e^{-y^2}}(0-e^{-x^2}(-2x))=\dfrac{2xe^{-x^2}}{1-e^{-y^2}}$

For the 2nd one we need to know the domain of integration. What are the limits? - Nov 15th 2011, 12:46 PMWevans2303Re: Integration/Differentiation help.
Oh god i've totally messed this up.

It's the other way round, integrate the first differentiate the second, sorry to have wasted your time.

If you're still in the mood to help, it would be the double integral of 24y(1-x-y ) with limits 0,1 for both x and y. - Nov 15th 2011, 01:01 PMtom@ballooncalculusRe: Integration/Differentiation help.
... whereas, if y is a function of x...

http://www.ballooncalculus.org/draw/diffProd/five.png

... where (key in spoiler) ...

__Spoiler__:

The second...

http://www.ballooncalculus.org/draw/diffProd/fivea.png

I'll maybe change it to use the limits.

Here we are, then...

http://www.ballooncalculus.org/draw/diffProd/fiveb.png

But that would still be integrating the second?!

__________________________________________________ __________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - Nov 15th 2011, 01:40 PMWevans2303Re: Integration/Differentiation help.
- Nov 15th 2011, 02:26 PMtom@ballooncalculusRe: Integration/Differentiation help.
Ok, and is your first expression a fraction as TES was guessing? Either way, this looks dodgy (i.e. non-elementary, involving the error function).

And in the second, is y a function of x? - Nov 15th 2011, 03:08 PMWevans2303Re: Integration/Differentiation help.
- Nov 16th 2011, 01:48 AMtom@ballooncalculusRe: Integration/Differentiation help.
int 0 to 1 int 0 to 1 (1-e^(-x^2))(1-e^(-y^2)) dy dx - Wolfram|Alpha

I.e...

http://www.ballooncalculus.org/draw/double/four.png

To differentiate f(x.y) with respect to (e.g.) x, expand and differentiate term by term, treating y as constant.

__________________________________________________ ____________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - Nov 16th 2011, 03:45 AMWevans2303Re: Integration/Differentiation help.