(d^2)/(dx^2)(sqrt(1+1/(x^4)))

解答

\frac{d ^{2}}{d x ^{2}} (1 + \frac{1}{x ^{4}})

\frac{2 ( 5 x ^{4} + 3 )}{x ^{4} ( x ^{4} + 1 ) x ^{4} + 1}

求解步骤

\frac{d ^{2}}{d x ^{2}} (1 + \frac{1}{x ^{4}})

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

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

\frac{d}{d x} (- \frac{2}{x ^{3} x ^{4} + 1}) = \frac{2 ( 5 x ^{4} + 3 )}{x ^{4} ( x ^{4} + 1 ) x ^{4} + 1}

= \frac{2 ( 5 x ^{4} + 3 )}{x ^{4} ( x ^{4} + 1 ) x ^{4} + 1}