3.5-bo'lim : Trig funksiyalarining hosilalari
8. \(y = 6 + 4\sqrt x \,\csc \left( x \right)\) ni farqlang.
Yechim
Bu erda ikkinchi muddat uchun mahsulot qoidasini talab qiladigan lotinni olishdan boshqa ko'p narsa qilish kerak emas.
\[y' = 4\left( {{\textstyle{1 \over 2}}} \right){x^{ - \,\,\frac{1}{2}}}\,\csc \left( x \right) + 4\sqrt x \,\left( { - \csc \left( x \right)\cot \left( x \right)} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{2{x^{ - \,\,\frac{1}{2}}}\,\csc \left( x \right) - 4\sqrt x \,\csc \left( x \right)\cot \left( x \right)}}\]