(d^3)/(dx^3)(e^{x^2})

解

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

2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

解答ステップ

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

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

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

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

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

\frac{d}{d x} (2 (2 e^{x^{2}} x^{2} + e^{x^{2}})) = 2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

= 2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)