Whats the derivative of sin^2(theta)?

Thread starter M. next
Start date May 10, 2012
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Derivative

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To find the derivative of sin^2(theta) with respect to time, apply the chain rule. The derivative is calculated as d/dt(sin^2(theta)) = d/dθ(sin^2(theta)) * dθ/dt. This results in the expression 2sin(theta)cos(theta) * (dθ/dt). The final answer confirms the application of the chain rule in this context.

May 10, 2012

M. next

but i need the derivative wrt time where theta depends on time

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May 10, 2012

Mark44

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M. next said:

but i need the derivative wrt time where theta depends on time

Use the chain rule.
$$\frac{d}{dt}sin^2(\theta) = \frac{d}{d\theta}sin^2(\theta)\cdot \frac{d\theta}{dt} = ? $$

May 10, 2012

M. next

then it is simply 2sin(theta)cos(theta)*(theta dot)

May 11, 2012

Mark44

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Yes, that's it.

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