derivative x*sin(4/x)

解

導関数

x \cdot sin (\frac{4}{x})

sin (\frac{4}{x}) - \frac{4 cos ( \frac{4}{x} )}{x}

解答ステップ

\frac{d}{d x} (x sin (\frac{4}{x}))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (\frac{4}{x})

= \frac{d x}{d x} sin (\frac{4}{x}) + \frac{d}{d x} (sin (\frac{4}{x})) x

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (\frac{4}{x})) = - \frac{4 cos ( \frac{4}{x} )}{x ^{2}}

= 1 \cdot sin (\frac{4}{x}) + (- \frac{4 cos ( \frac{4}{x} )}{x ^{2}}) x

簡素化

1 \cdot sin (\frac{4}{x}) + (- \frac{4 cos ( \frac{4}{x} )}{x ^{2}}) x : sin (\frac{4}{x}) - \frac{4 cos ( \frac{4}{x} )}{x}

= sin (\frac{4}{x}) - \frac{4 cos ( \frac{4}{x} )}{x}