# Why aren't the derivatives equal?

1. Oct 14, 2015

### Calpalned

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

2. Relevant equations
see above

3. The attempt at a solution
After getting $v = |\frac{dz}{dt}|=\frac{3}{t^2+1}$ why can't I simply take the derivative of that with respect to $t$ to get the acceleration?
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2. Oct 14, 2015

### Staff: Mentor

The notation is a little weird. What they're calling v is actually the magnitude of the velocity, not the velocity itself, and $\frac{dz}{dt}$ is the velocity. To get the acceleration, you need to differentiate the velocity (not its magnitude) with respect to t.

3. Oct 14, 2015

### Calpalned

4. Oct 14, 2015

### Calpalned

Okay, so simply put the derivative of the magnitude of velocity is not the magnitude of acceleration? $\frac{d}{dt}(|\frac{dz}{dt}|)\neq|\frac{d^2 z}{dt^2}|$

5. Oct 14, 2015

### Calpalned

But the question asks for the magnitude of acceleration

6. Oct 14, 2015

### Staff: Mentor

7. Oct 14, 2015

### Staff: Mentor

Right, but they first have to get the acceleration, and then get its magnitude.

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