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Problem 29 Easy Difficulty

If $ H(\theta) = \theta $ sin $ \theta, $ find $ H'(\theta) $ and $ H"(\theta). $


$$H^{\prime \prime}(\theta)=\theta(-\sin \theta)+(\cos \theta) \cdot 1+\cos \theta=-\theta \sin \theta+2 \cos \theta$$

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Video Transcript

we're so when you married here. So we her Rita which is equal to data sign Fada. So what's take the first derivative? And we use the product rules. We get the derivative of data I'm sign, plus data times the derivative of sign. And this gives us signed data Rita Co sign Next. We're going to take the second derivative using the first derivative so they get co sign, plus the derivative of data we'll sign, plus data turns the derivative of co sign. And this gives us one negative sign, which gives us two SCO sign minus data sign.