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Problem 15 Easy Difficulty

Differentiate.

$ f(\theta) = \theta $ cos $ \theta $ sin $ \theta $

Answer

$f^{\prime}(\theta)=1 \cos \theta \sin \theta+\theta(-\sin \theta) \sin \theta+\theta \cos \theta(\cos \theta)=\cos \theta \sin \theta-\theta \sin ^{2} \theta+\theta \cos ^{2} \theta$ $=\sin \theta \cos \theta+\theta\left(\cos ^{2} \theta-\sin ^{2} \theta\right)=\frac{1}{2} \sin 2 \theta+\theta \cos 2 \theta$

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Video Transcript

it's clear. So when you right here. So we're gonna take the derivative of data. Co. Sign time sign. This is gonna be equal to the over D Saito data Times co sign I'm signed. Let's stay tha d over. D aceto of co Sign time Signed list data D over defeat Ill of sign Times CO Something This becomes equal to co sign. I'm sign minus data signed. Square plus Data Co sign Square, which is equal to co sign I'm signed. WAAS Data Terms Co. Sign square minus sign square and we're using our double angle trick identities, which gives us one have sign to data plus data co sign to data.