derivative of sqrt(x^5)-\sqrt[4]{x^9}

解

\frac{d}{d x} (x^{5} - 4 x^{9})

\frac{5 x ^{\frac{3}{2}}}{2} - \frac{9 x ^{\frac{5}{4}}}{4}

解答ステップ

\frac{d}{d x} (x^{5} - 4 x^{9})

和/差の法則を適用:

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

= \frac{d}{d x} (x^{5}) - \frac{d}{d x} (4 x^{9})

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

\frac{d}{d x} (4 x^{9}) = \frac{9 x ^{\frac{5}{4}}}{4}

= \frac{5 x ^{\frac{3}{2}}}{2} - \frac{9 x ^{\frac{5}{4}}}{4}