Time derivatives

Fellowroot

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)?

nucl34rgg

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

HallsofIvy

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].

Similar discussions for: Time derivatives
Thread	Forum	Replies
Time Derivatives of Unit Vectors	Calculus & Beyond Homework	2
looking for Lagrangian Systems with Higher Order Time Derivatives	Classical Physics	0
Why no EOM in QFT with higher than second order derivatives in time and space?	Quantum Physics	4
Help understanding derivatives of time; chain rule.	Introductory Physics Homework	1
time derivatives where there's no explicit time dependence	Calculus	2

Fellowroot	Time derivatives 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)?

nucl34rgg	Well, assuming theta is a function of time, you must use the chain rule!

HallsofIvy Recognitions: Gold Member Science Advisor Staff Emeritus	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].