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

解

導関数

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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