Taking the derivative of a function of a function

[ArisMartinez]

Summary:: According to Yale’s University PHYS: 200:
v*(dv/dt) = d(v^2/2)/dt

Could someone explain how has he reached that conclusion? He claims to be some standard derivation rules, but I can’t find anything about it.

As much as I can tell: (dv/dt)* v = v’ * v = a* v

thanks!

[Moderator's note: moved from a technical forum.]

 

[fresh_42]

Do you know the chain rule? What is $\dfrac{d}{dt} v(t)^2$?

 

[ArisMartinez]

Do you know the chain rule? What is $\dfrac{d}{dt} v(t)^2$?

I do! But I coudn not see why I had to use the chain rule here. (I see it clearer when I have ie. (cos(x))^sin(x))

but I do now! I’m not used to the physics notation of derivatives. But that was helpful, so thanks a lot.

 

[Mark44]

Could someone explain how has he reached that conclusion? He claims to be some standard derivation rules, but I can’t find anything about it.

If you're taking the derivative of a function of a function; e.g., something like this: $\frac d{dx} f(g(x))$, the differentiation rule that should come to mind is the chain rule.