Whats the derivative of sin^2(theta)?

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Homework Help Overview

The discussion revolves around finding the derivative of sin²(θ) with respect to time, considering that θ is a function of time. The subject area is calculus, specifically focusing on differentiation and the application of the chain rule.

Discussion Character

  • Mathematical reasoning, Exploratory

Approaches and Questions Raised

  • Participants explore the application of the chain rule for differentiating sin²(θ) with respect to time. There is a focus on how to express the derivative in terms of θ and its rate of change over time.

Discussion Status

Some participants have confirmed the application of the chain rule and provided expressions related to the derivative. There appears to be a shared understanding of the approach, though no explicit consensus on the final expression is reached.

Contextual Notes

Participants are working under the assumption that θ is a time-dependent variable, which influences the differentiation process. The discussion does not clarify any specific constraints or additional information regarding the problem.

M. next
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but i need the derivative wrt time where theta depends on time
 
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M. next said:
but i need the derivative wrt time where theta depends on time

Use the chain rule.
$$\frac{d}{dt}sin^2(\theta) = \frac{d}{d\theta}sin^2(\theta)\cdot \frac{d\theta}{dt} = ? $$
 
then it is simply 2sin(theta)cos(theta)*(theta dot)
 

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