derivative of x/(sin(x))

解

\frac{d}{d x} (\frac{x}{sin ( x )})

csc (x) - x cot (x) csc (x)

解答ステップ

\frac{d}{d x} (\frac{x}{sin ( x )})

簡素化

\frac{x}{sin ( x )} : x csc (x)

= \frac{d}{d x} (x csc (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = csc (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot csc (x) + (- cot (x) csc (x)) x

簡素化

= csc (x) - x cot (x) csc (x)