Question

Given: v \times \frac{dv}{dx}
How would you determine that this is equal to: \frac{d}{dx} \left ( \frac{v^2}{2} \right ) ?

Answer 1

Given: \[v \times \frac{dv}{dx}\]
How would you determine that this is equal to: \[\frac{d}{dx} \left ( \frac{v^2}{2} \right )\]

Answer 2

Betting on the power rule and the chain rule (assuming v is some function of x, of course. and even if it isn't, this would still hold... ^_^ )

Answer 3

your question is perhaps what is the integral of vdv ?

Answer 4

\(v \times \dfrac{dv}{dx}=d\int v \times \dfrac{dv}{dx}=\dfrac{d}{dx}\int v dv=\dfrac{d}{dx}(\dfrac{v^2}{2}) \)