# Homework Help: Is the derivative in my textbook correct here?

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1. Sep 12, 2016

### whitejac

1. The problem statement, all variables and given/known data

2. Relevant equations
d/dx

3. The attempt at a solution
d/dx (T) = d/dx(1/2mx'2) = mx''
d/dx(U) = d/dx(1/2kx2) = kx' ≠ kx

It's probably me who made an error because I know that that equation (2.3) is the one I should be getting, but I don't understand how they did it because potential energy relies on position, so the derivative has to be a velocity vector.

2. Sep 12, 2016

### Staff: Mentor

Here x is a function of t and the derivatives should be with respect to t. That's what x' implies.

3. Sep 12, 2016

### Staff: Mentor

(2.6) shows differentiation with respect to time. Your working is erroneously using differentiation with respect to x.

4. Sep 12, 2016

### whitejac

Oh right, it's x(t)... I guess the caffeine hasn't kicked in because that was really basic. Thank you!

5. Sep 12, 2016

### Staff: Mentor

6. Sep 12, 2016

### Staff: Mentor

I think (2.3) starts out as $m \ddot x \dot x + k x \dot x = 0$ and the common factor $\dot x$ can be cancelled from both sides.