# Time derivatives

by Fellowroot
Tags: derivatives, time
 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)?
 P: 128 Well, assuming theta is a function of time, you must use the chain rule!
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,708 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 $(\theta')^2$. The derivative of any $(f(t))^2$ with respect to t is $2f(t)f'(t)$, by the chain rule, so the derivative of $(\theta(t)')^2$ is $2(\theta')(\theta'')$.

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