derivative of sqrt(xsin(x))

解

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

\frac{sin ( x ) + x cos ( x )}{2 x sin ( x )}

解答ステップ

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

連鎖法則を適用:

\frac{1}{2 x sin ( x )} \frac{d}{d x} (x sin (x))

= \frac{1}{2 x sin ( x )} \frac{d}{d x} (x sin (x))

\frac{d}{d x} (x sin (x)) = sin (x) + x cos (x)

= \frac{1}{2 x sin ( x )} (sin (x) + x cos (x))

簡素化

\frac{1}{2 x sin ( x )} (sin (x) + x cos (x)) : \frac{sin ( x ) + x cos ( x )}{2 x sin ( x )}

= \frac{sin ( x ) + x cos ( x )}{2 x sin ( x )}