derivative y=(e^{4x^2}+1)/8

解

導関数

y = \frac{e ^{4 x^{2}} + 1}{8}

e^{4 x^{2}} x

解答ステップ

\frac{d}{d x} (\frac{e ^{4 x^{2}} + 1}{8})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{8} \frac{d}{d x} (e^{4 x^{2}} + 1)

和/差の法則を適用:

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

= \frac{1}{8} (\frac{d}{d x} (e^{4 x^{2}}) + \frac{d}{d x} (1))

\frac{d}{d x} (e^{4 x^{2}}) = e^{4 x^{2}} \cdot 8 x

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

= \frac{1}{8} (e^{4 x^{2}} \cdot 8 x + 0)

簡素化

\frac{1}{8} (e^{4 x^{2}} \cdot 8 x + 0) : e^{4 x^{2}} x

= e^{4 x^{2}} x