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

Question

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

anonymous · Answer

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

terenzreignz · Answer

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... ^_^ )

shubhamsrg · Answer

your question is perhaps what is the integral of vdv ?

hartnn · Answer

$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}) $