Solving a Differential Problem with Chain Rule

[Hakins90]

Hmmm its really a maths question.

In my textbook it says - "$$v \frac {dv}{dx} = \frac {d}{dx} ( \frac 12 v^2)$$ by the chain rule."

I can't see how they made this jump from the L.H.S. to the R.H.S.

Thanks

 

[rock.freak667]

Well if you differentiate the RHS w.r.t.x then you'll get $\frac{1}{2}*2v\frac{dv}{dx} = v\frac{dv}{dx}$ so it is really a matter of writing an equivalent statement on the RHS

 

[Hakins90]

Hmmm

I thought $$\frac {d}{dx} ( \frac 12 v^2) = 2 * \frac 12 * v = v$$ and not $$v \frac {dv}{dx}$$

Sorry if I am being stupid :D

 

[Hurkyl]

$$\frac {d}{dx} ( \frac 12 v^2) = 2 * \frac 12 * v$$

So you're telling me that dv/dx = 1? Why do you think that?