(d^4)/(dx^4)(2e^{x^2})

解

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

4 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

解答ステップ

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

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

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

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

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

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

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

\frac{d}{d x} (4 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)) = 4 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

= 4 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})