Ok I found your problem, we can continue.

Just give me a moment

The mistake you made was the subscript Uxx means the second derivative of the function and not only the first

So we take one derivative, then repeating again for the next one related to x

remember f ' (x) = e^x = e^x and f'(x)= e^x^2 = 2x*e^x^2

u(x,t)= t^3e^(-x^2/u)

-3e^(-x^2/u)

u '(x)= t^3*(-6x/u)e^(-x^2/u)

Answer: u ''(x)= t^3*(-36x^2/u^2)e^(-x^2/u)

Is it t cube * (-36x^2/u^2)*e^(-x^2/u)

ah excuse the last answer there is a negative sign error

u ''(x)= t^3*(36x^2/u^2)e^(-x^2/u)

can you please take a picture and attach it. I confussed

because the -2x multiplies down again so the negative cancels

ok I'll draw it out again

Variable 'u' is not defined in the answer

it shouldn't be there ("u").

I drew it out and had noticed another error, the three got mixed into the multiplication while carrying terms by mistake.

Should be the answer to the question

First derivative

Second derivative (Answer)

hmm, what does your textbook say?

It's attached to the x^2 as a coefficient so should carry with the term

Sir, The answer should only have variables x and t, u is not a variable its the function name. the answer should only have x and t.

I see what you mean

my best guess is you substitute in u(x,t) again in the exponential before doing the derivative

Ok.

Can you please give me the answer.

We can try using this to substitute for the answer starting with some of the work before

I will check thank you.

Just organizing more so can help

If you substitute the value for u(x,t) it would get repetitive unless using the variable u, so there'd have to be something left in variable form, should be as simple as we can get without it becoming messy

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