derivative of 2x^{3/2}+4x^{5/4}

解

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

3 x^{\frac{1}{2}} + 5 x^{\frac{1}{4}}

解答ステップ

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

和/差の法則を適用:

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

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

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

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

= 3 x^{\frac{1}{2}} + 5 x^{\frac{1}{4}}