(d^2)/(dx^2)(1/(ln(x)))

解

\frac{d ^{2}}{d x ^{2}} (\frac{1}{ln ( x )})

\frac{ln ( x ) + 2}{x ^{2} ln ^{3} ( x )}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (\frac{1}{ln ( x )})

\frac{d}{d x} (\frac{1}{ln ( x )}) = - \frac{1}{x ln ^{2} ( x )}

= \frac{d}{d x} (- \frac{1}{x ln ^{2} ( x )})

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

= \frac{ln ( x ) + 2}{x ^{2} ln ^{3} ( x )}