найти производную ln(sin x/2 ). Created by gabdullina. algebra-ru

2 )...

Kami924

ln(sin x/2 ) $(ln(sin \frac {x}{2}))'=\frac{(sin \frac {x}{2})'}{sin \frac {x}{2}}=\frac {cos\frac {x}{2} *(\frac {x}{2})'}{sin \frac {x}{2}}=\frac {cos\frac {x}{2}}{2sin \frac {x}{2}}=\frac {tg \frac{x}{2}}{2}$

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dtnth

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=(sin x/2)'/sin x/2= $\frac{-\frac{1}{2}cos\frac{x}{2}}{sin\frac{x}{2}}=-\frac{1}{2}сtg \frac{x}{2}$

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