derivative of 4x+2x^2sin(1/x)

解

\frac{d}{d x} (4 x + 2 x^{2} sin (\frac{1}{x}))

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

解答ステップ

\frac{d}{d x} (4 x + 2 x^{2} sin (\frac{1}{x}))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x) + \frac{d}{d x} (2 x^{2} sin (\frac{1}{x}))

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

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

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