Follow the derivation of the following equations for deflections of a beam, filling in all the required assumptions and steps in the derivations. EIv'' = M EIv''' =V EIv'''' = ?q where v is the deflection of the beam, E is Young's modulus, I is the second moment of inertia of the beam cross section about the neutral axis, M is the moment at a specific location x along the length of the beam, V is the shear force at the same point, and q is the distributed load (force/per unit length) at the same point.