derivative of 9x^{7/5}-5x^2+10^4

解

\frac{d}{d x} (9 x^{\frac{7}{5}} - 5 x^{2} + 1 0^{4})

- 10 x + \frac{63 x ^{\frac{2}{5}}}{5}

解答ステップ

\frac{d}{d x} (9 x^{\frac{7}{5}} - 5 x^{2} + 1 0^{4})

簡素化

9 x^{\frac{7}{5}} - 5 x^{2} + 1 0^{4} : 9 x^{\frac{7}{5}} - 5 x^{2} + 10000

= \frac{d}{d x} (9 x^{\frac{7}{5}} - 5 x^{2} + 10000)

和/差の法則を適用:

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

= \frac{d}{d x} (9 x^{\frac{7}{5}}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (10000)

\frac{d}{d x} (9 x^{\frac{7}{5}}) = \frac{63 x ^{\frac{2}{5}}}{5}

\frac{d}{d x} (5 x^{2}) = 10 x

\frac{d}{d x} (10000) = 0

= \frac{63 x ^{\frac{2}{5}}}{5} - 10 x + 0

簡素化

= - 10 x + \frac{63 x ^{\frac{2}{5}}}{5}