derivative sqrt(3+5sin(x))

解

導関数

3 + 5 sin (x)

\frac{5 cos ( x )}{2 3 + 5 sin ( x )}

解答ステップ

\frac{d}{d x} (3 + 5 sin (x))

連鎖法則を適用:

\frac{1}{2 3 + 5 sin ( x )} \frac{d}{d x} (3 + 5 sin (x))

= \frac{1}{2 3 + 5 sin ( x )} \frac{d}{d x} (3 + 5 sin (x))

\frac{d}{d x} (3 + 5 sin (x)) = 5 cos (x)

= \frac{1}{2 3 + 5 sin ( x )} \cdot 5 cos (x)

簡素化

\frac{1}{2 3 + 5 sin ( x )} \cdot 5 cos (x) : \frac{5 cos ( x )}{2 3 + 5 sin ( x )}

= \frac{5 cos ( x )}{2 3 + 5 sin ( x )}