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Problem 11 Easy Difficulty

Differentiate.

$ f(\theta) = \frac {sin \theta }{1 + cos \theta } $

Answer

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

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Video Transcript

it's clear. Someone name right here. So we're gonna differentiate of if they'd eyes equal to sign beta. Well, everyone plus co sign. We're gonna start with the caution rule, which gives us de over de Feydeau. Sign data was one class is co sign of beta minus. Be over. D fada, have co sign data. I'm signed data well over one plus go sign the U. S. Square. This gives us co sign Data plus co sign square plus sign square over one plus co sign Data Square. This simplifies further to co sign plus one over one plus Go Son Data Square, which is equal to one plus one over one plus post signed data.