derivative f(x)=x^2-2/x+3*sin(2x)

解

導関数

f (x) = x^{2} - \frac{2}{x} + 3 \cdot sin (2 x)

2 x + \frac{2}{x ^{2}} + 6 cos (2 x)

解答ステップ

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

和/差の法則を適用:

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

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

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

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

\frac{d}{d x} (3 sin (2 x)) = 6 cos (2 x)

= 2 x - (- \frac{2}{x ^{2}}) + 6 cos (2 x)

簡素化

= 2 x + \frac{2}{x ^{2}} + 6 cos (2 x)