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Time derivatives

by Fellowroot
Tags: derivatives, time
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Mar9-12, 12:34 PM
P: 42
1. The problem statement, all variables and given/known data

My question is how do I take the time derivative of (theta dot)^2?

2. Relevant equations

3. The attempt at a solution

Is the answer just 2(theta double dot)^1 or do you use chain rule 2(theta dot)*(theta double dot)?
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Mar9-12, 12:40 PM
P: 129
Well, assuming theta is a function of time, you must use the chain rule!
Mar9-12, 12:40 PM
Sci Advisor
PF Gold
P: 39,497
I take that your "dot" refers to differentiation with respect to time, t,- I will use a prime since it is simpler here- and you are asking about the derivative of [itex](\theta')^2[/itex].

The derivative of any [itex](f(t))^2[/itex] with respect to t is [itex]2f(t)f'(t)[/itex], by the chain rule, so the derivative of [itex](\theta(t)')^2[/itex] is [itex]2(\theta')(\theta'')[/itex].

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