Differentiation of a formula with two variables, Mathematics

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I would like to calculate the high point of a mathematical formula with two unknown variables. At the same time I made the 1st derivation of the function. How can I best program this?

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Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)

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