derivative of 1+(3/2 x^{(1/2})^2)

解

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

\frac{9}{4}

十進法表記

2.25

解答ステップ

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

簡素化

1 + (\frac{3}{2} x^{(\frac{1}{2})})^{2} : 1 + \frac{9 x}{4}

= \frac{d}{d x} (1 + \frac{9 x}{4})

和/差の法則を適用:

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

= \frac{d}{d x} (1) + \frac{d}{d x} (\frac{9 x}{4})

\frac{d}{d x} (1) = 0

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

= 0 + \frac{9}{4}

簡素化

= \frac{9}{4}