derivative of x^2+1/(2x-3x)

解

\frac{d}{d x} (x^{2} + \frac{1}{2 x} - 3 x)

2 x - \frac{1}{2 x ^{2}} - 3

解答ステップ

\frac{d}{d x} (x^{2} + \frac{1}{2 x} - 3 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{1}{2 x}) - \frac{d}{d x} (3 x)

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

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

\frac{d}{d x} (3 x) = 3

= 2 x - \frac{1}{2 x ^{2}} - 3