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Question: How to use Leibniz rule to find the diffrentiation of an integral with variable domain while inside the integral I have a multivariable function

Question:How to use Leibniz rule to find the diffrentiation of an integral with variable domain while inside the integral I have a multivariable function

donya 8 Maple 14
May 30 2011
2

I want to use leibniz rule to differentiate the following Integral with variable domain:
A :=(t,x) -> int(Yt^2, x = 0 .. zeta);
Yt and zeta are defined as:
alias(zeta=zeta(t));
Yt:=(t,x)->diff(y(t,x),t);
When I want maple to derive D[1](A(t,x)), its answer is:
2*D[1](Yt)*Yt*Zeta+Yt^2*D[1](Zeta)
Although it uses Leibniz rule correctly, it dose not take Yt as a function of x by mistake. 2*D[1](Yt)*Yt*Zeta should had been derived as int(2*D[1](Yt)*Yt,x=0..zeta).
The problem is that Maple forgets than Yt is still a function of (t,x). Moreover, if I mentioned it in the deffenition of A(t,x) function, It dose not use Leibniz rule anymore.
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