Partial Derivatives Calculus 3

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Oct 11th, 2015

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)

Oct 11th, 2015

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


Oct 11th, 2015

ah excuse the last answer there is a negative sign error

Oct 11th, 2015

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


Oct 11th, 2015

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


Oct 11th, 2015

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

Oct 11th, 2015

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

Oct 11th, 2015

ok I'll draw it out again

Oct 11th, 2015

Variable 'u' is not defined in the answer

Oct 11th, 2015

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


Oct 11th, 2015

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)



Oct 11th, 2015
first_derivative.png
second_derivative.png
first_derivative.png
second_derivative.png
second_derivative.png

hmm, what does your textbook say?

Oct 11th, 2015

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

Oct 11th, 2015

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. 

Oct 11th, 2015

I see what you mean

Oct 11th, 2015

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

Oct 11th, 2015

Ok.

Oct 11th, 2015

Can you please give me the answer.

Oct 11th, 2015

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


Oct 11th, 2015
substitute.png

I will check thank you.

Oct 11th, 2015

Just organizing more so can help



Oct 11th, 2015
substitute.png

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

Oct 11th, 2015

Ok.

Oct 11th, 2015

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Oct 11th, 2015
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