derivative y=6+4sqrt(x)csc(x)

解

導関数

y = 6 + 4 x csc (x)

4 (- x cot (x) csc (x) + \frac{csc ( x )}{2 x})

解答ステップ

\frac{d}{d x} (6 + 4 x csc (x))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (6) + \frac{d}{d x} (4 x csc (x))

\frac{d}{d x} (6) = 0

\frac{d}{d x} (4 x csc (x)) = 4 (\frac{csc ( x )}{2 x} - x cot (x) csc (x))

= 0 + 4 (\frac{csc ( x )}{2 x} - x cot (x) csc (x))

簡素化

= 4 (- x cot (x) csc (x) + \frac{csc ( x )}{2 x})