Time Derivatives: Taking the Time Derivative of (theta dot)^2

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To take the time derivative of (theta dot)^2, the chain rule must be applied. The correct derivative is 2(theta dot)(theta double dot), where theta dot represents the first derivative of theta with respect to time and theta double dot represents the second derivative. This follows the general rule that the derivative of (f(t))^2 is 2f(t)f'(t). Therefore, the time derivative of (\theta')^2 is 2(\theta')(\theta''). Understanding this process is crucial for correctly applying derivatives in physics problems.
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Homework Statement



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


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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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Well, assuming theta is a function of time, you must use the chain rule!
 
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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