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

解

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

e^{2 (x - 1)^{2}} \cdot 4 (x - 1) + \frac{1 - 2 x ^{3}}{( 1 + x ^{3} ) ^{2}}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (e^{2 (x - 1)^{2}}) = e^{2 (x - 1)^{2}} \cdot 4 (x - 1)

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

= e^{2 (x - 1)^{2}} \cdot 4 (x - 1) + \frac{1 - 2 x ^{3}}{( 1 + x ^{3} ) ^{2}}