Beam Deflection and Shearing Force (Civil Engineering)

A civil structural engineer is evaluating the internal forces on a $12\text{ m}$ highway bridge girder supporting a non-uniform traffic load. The internal bending moment distribution $M(x)$ along the span of the beam (measured in $\text{kN}\cdot\text{m}$ for $x \in [0, 12]$) is modeled by:

In structural mechanics, the internal shear force $V(x)$ (measured in $\text{kN}$) is the spatial rate of change of the bending moment:

1. Pre-process the radical denominator term in $M(x)$ using negative and rational exponent laws.
2. Differentiate $M(x)$ to find the analytical expression for the internal shear force $V(x)$.
3. Post-process your derivative into standard radical notation, and evaluate the internal shear force at the support coordinate $x = 0\text{ m}$ and at the mid-span $x = 5\text{ m}$.