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

解

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

8 (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}} (4 e^{x^{2}})

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

= \frac{d ^{3}}{d x ^{3}} (8 e^{x^{2}} x)

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

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

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

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

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

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