derivative y=(9(1-sin(x)))/(2cos(x))

解

導関数

y = \frac{9 ( 1 - sin ( x ) )}{2 cos ( x )}

\frac{9 ( - 1 + sin ( x ) )}{2 cos ^{2} ( x )}

解答ステップ

\frac{d}{d x} (\frac{9 ( 1 - sin ( x ) )}{2 cos ( x )})

定数を除去:

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

= \frac{9}{2} \frac{d}{d x} (\frac{1 - sin ( x )}{cos ( x )})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{9}{2} \cdot \frac{\frac{d}{d x} ( 1 - sin ( x ) ) cos ( x ) - \frac{d}{d x} ( cos ( x ) ) ( 1 - sin ( x ) )}{( cos ( x ) ) ^{2}}

\frac{d}{d x} (1 - sin (x)) = - cos (x)

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

= \frac{9}{2} \cdot \frac{( - cos ( x ) ) cos ( x ) - ( - sin ( x ) ) ( 1 - sin ( x ) )}{( cos ( x ) ) ^{2}}

簡素化

\frac{9}{2} \cdot \frac{( - cos ( x ) ) cos ( x ) - ( - sin ( x ) ) ( 1 - sin ( x ) )}{cos ^{2} ( x )} : \frac{9 ( - 1 + sin ( x ) )}{2 cos ^{2} ( x )}

= \frac{9 ( - 1 + sin ( x ) )}{2 cos ^{2} ( x )}