Problem with partial derivatives

[aliyuaziz]

Hello, kindly assist with how to carry out partial derivative of F(u(x),x) := (du/dx)^3+u^2*sin(x)+4*u

I tried to use functional_diff function but it always ignored the first term. Kindly assist.

Best regards,
Aliyu A. Aziz

[MrMage]

Hello,

Please try this: Define e.g. u(x):=exp(x), then

F(u,x):=diff(u(x),x)^3+u(x)^2*sin(x)+4*u(x)

Regards

Daniel

[aliyuaziz]

Many thanks for the quick response. I am able to go forward pass the definition. My next challenge is that the functional_diff is still neglecting the first term as follows:

u(x):=exp(x)
F(u,x):=diff(u,x)^3+u(x)^2*sin(x)+4*u(x)
function_diff(F)
function_diff(F)(u)

Thanks for your assistance.

Best regards,
Aliyu A. Aziz

[MrMage]

Please tell me what exactly you want to achieve. I don't get it yet.

[aliyuaziz]

Thanks, I am trying to compute variation of functionals, such as follows:
 
If F(u(x),x):=(du/dx)^3+u^2*sin(x)+4*u.

Then delta_F := 3(du/dx)^2  delta_(du/dx) + 2*u*sin(x) delta_u + 4delta_u

Which is equivalent to
   
                 3(du/dx)^2 d(delta_u /dx) + 2*u*sin(x) delta_u + 4delta_u

Note that delta_ represents the delta sign.

I trust the above clarifies the  challenge I am facing and look forward to hearing from you.

Best regards,
Aliyu A. Aziz

                                 

[MrMage]

I am not the CAS developer, but I doubt that calculating the derivative of a functional is possible in PocketCAS, sorry.