derivative of 5x^3+x^2+1/x

解

\frac{d}{d x} (5 x^{3} + x^{2} + \frac{1}{x})

15 x^{2} + 2 x - \frac{1}{x ^{2}}

解答ステップ

\frac{d}{d x} (5 x^{3} + x^{2} + \frac{1}{x})

和/差の法則を適用:

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

= \frac{d}{d x} (5 x^{3}) + \frac{d}{d x} (x^{2}) + \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

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

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

= 15 x^{2} + 2 x - \frac{1}{x ^{2}}