How do I find the derivative of d(x(t)2)/dt?

[tomwilliam]

Homework Statement

d(x(t)²)/dt

Homework Equations

The Attempt at a Solution

I guess that this should be:

2x(dx/dt)
but I'm not sure how to justify it:
u= x
d(u²)/du = 2u

(d(u²)/du)(du/dt) = d(u²)/dt

So 2u(du/dt) = 2x(dx/dt)
Is this right?

 

[HallsofIvy]

Yes, that's just the chain rule.

 

[tiny-tim]

hi tomwilliam!

you don't need to use substitution …

just say d(x(t)²)/dt = d(x(t)²)/d(x(t)) d(x(t))/dt = 2x dx/dt

 

[tomwilliam]

Oh yes. Thanks for that.