derivative 4x^{5/4}+8x^{3/2}+9x

解

導関数

4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 9 x

5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 9

解答ステップ

\frac{d}{d x} (4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 9 x)

和/差の法則を適用:

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

= \frac{d}{d x} (4 x^{\frac{5}{4}}) + \frac{d}{d x} (8 x^{\frac{3}{2}}) + \frac{d}{d x} (9 x)

\frac{d}{d x} (4 x^{\frac{5}{4}}) = 5 x^{\frac{1}{4}}

\frac{d}{d x} (8 x^{\frac{3}{2}}) = 12 x^{\frac{1}{2}}

\frac{d}{d x} (9 x) = 9

= 5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 9