Tricky Partial Differential problem

Hi all, I wish to verify

with the shorthand notations being and for the following expression

where k is a constant and f is continous on the real line ( I actually dont understrand what that 'f' bit means)

Can anyone give me a clue as how to tackle this one? Do I integrate the integrand first and then find the derivatives ? If so, how does one tackle the integrand with the infinity signs etc?

Thanks, tips will be appreciated.

Looking forward to hearing from some one.

Bugatti79

Tricky Partial Differential problem

Loooking at that Leibniz expression...i dont know how one would tackle the problem because I believe the derivative of infinity is undefined ( I am referring to ). A function must be continous to be differentiable....

bugatti79

Tricky Partial Differential problem

I dont know where I am gone wrong.

Using the chain rule I calculate for

and

and the product rule for since t is on both numerator and denominator

Can anyone confirm im going correct so far? (Happy)

Tricky Partial Differential problem

Still cant get

I dont know wheter im getting my algebra in a twist or my derivatives are still wrong.

I recalculate

and for I use product rule in the numerator

and qoutient rule for

If these derivatives can be confirmed correct then I know the rest is basic algebra....

Thanks

bugatti79