derivative f(x)=((sin(x))/x)^2

解

導関数

f (x) = (\frac{sin ( x )}{x})^{2}

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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