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

解

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

1 - \frac{x}{2} + \frac{x ^{2}}{9}

解答ステップ

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

簡素化

x - (\frac{x}{2})^{2} + (\frac{x}{3})^{3} : x - \frac{x ^{2}}{4} + \frac{x ^{3}}{27}

= \frac{d}{d x} (x - \frac{x ^{2}}{4} + \frac{x ^{3}}{27})

和/差の法則を適用:

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

= \frac{d x}{d x} - \frac{d}{d x} (\frac{x ^{2}}{4}) + \frac{d}{d x} (\frac{x ^{3}}{27})

\frac{d x}{d x} = 1

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

\frac{d}{d x} (\frac{x ^{3}}{27}) = \frac{x ^{2}}{9}

= 1 - \frac{x}{2} + \frac{x ^{2}}{9}