What Mathematical Identity is Used in This Derivation?

[aaaa202]

Consider the equation on the attached picture. What mathematical identity for differential calculus (which I assume is used) is used to go from the LHS to the RHS? I tried invoking the product rule but couldn't get anywhere.

 

[TSny]

You're on the right track. Apply the product rule to the first term on the RHS and show that the entire RHS reduces to the LHS.

 

[TSny]

Or, if you really want to go from the LHS to the RHS then use ($\frac{dA}{dt}$$)\cdot$B = $\frac{d}{dt}$(A$\cdot$B) - A$\cdot$$\frac{dB}{dt}$ which is just the product rule rearranged.