derivative of ((sin(x)/(1+cos(x)))^2)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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