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

解

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

x^{4} - 6 x^{2} + 3

解答ステップ

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

簡素化

\frac{1}{5} x^{5} - 2 x^{3} + 3 x : \frac{x ^{5}}{5} - 2 x^{3} + 3 x

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

和/差の法則を適用:

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

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

\frac{d}{d x} (\frac{x ^{5}}{5}) = x^{4}

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

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

= x^{4} - 6 x^{2} + 3