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.
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?
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.
... whereas, if y is a function of x...
... where (key in spoiler) ...
Spoiler:
The second...
I'll maybe change it to use the limits.
Here we are, then...
But that would still be integrating the second?!
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int 0 to 1 int 0 to 1 (1-e^(-x^2))(1-e^(-y^2)) dy dx - Wolfram|Alpha
I.e...
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!