(d^4)/(dx^4)(3e^{x^2})

解答

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

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

求解步骤

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

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

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

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

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

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

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

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

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

4 y^{^{''}} - 4 y^{^{'}} + y = 0

n = 1 \sum \infty ln (\frac{1}{n ^{2}})

x \to 3 lim (\frac{x ^{2} - 1}{x - 3})

\frac{d v}{d t}

y^{2} \frac{d y}{d x} = y^{3} - x^{3}