derivative of 1/27 (x^5+2x^3)

解

\frac{d}{d x} (\frac{1}{27} (x^{5} + 2 x^{3}))

\frac{1}{27} (5 x^{4} + 6 x^{2})

解答ステップ

\frac{d}{d x} (\frac{1}{27} (x^{5} + 2 x^{3}))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{27} \frac{d}{d x} (x^{5} + 2 x^{3})

和/差の法則を適用:

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

= \frac{1}{27} (\frac{d}{d x} (x^{5}) + \frac{d}{d x} (2 x^{3}))

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

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

= \frac{1}{27} (5 x^{4} + 6 x^{2})