derivative of 3sqrt(sin(x))

解

\frac{d}{d x} (3 sin (x))

\frac{3 cos ( x )}{2 sin ( x )}

解答ステップ

\frac{d}{d x} (3 sin (x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (sin (x))

連鎖法則を適用:

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

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

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

= 3 \cdot \frac{1}{2 sin ( x )} cos (x)

簡素化

3 \cdot \frac{1}{2 sin ( x )} cos (x) : \frac{3 cos ( x )}{2 sin ( x )}

= \frac{3 cos ( x )}{2 sin ( x )}