The theoretical formula for my beam deflection is:
$ v(x) = \begin{cases} -\frac{Px}{48EI}(3L^2-4x^2), & 0\le x \le {L\over2}\\ -\frac{P(x-L)}{48EI}(L^2-8Lx+4x^2), & {L\over2}\lt x \le L \end{cases}$
I need to derive the formulae for the slope $v'$, curvature $v''$ and $v'''$
Is this just a simply case of taking the first, second, and third derivative of the original equation? I know absolutely nothing about structural beams...