(d^2)/(dx^2)(ln(x^2+3x+15))

解

\frac{d ^{2}}{d x ^{2}} (ln (x^{2} + 3 x + 15))

\frac{- 2 x ^{2} - 6 x + 21}{( x ^{2} + 3 x + 15 ) ^{2}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (ln (x^{2} + 3 x + 15))

\frac{d}{d x} (ln (x^{2} + 3 x + 15)) = \frac{2 x + 3}{x ^{2} + 3 x + 15}

= \frac{d}{d x} (\frac{2 x + 3}{x ^{2} + 3 x + 15})

\frac{d}{d x} (\frac{2 x + 3}{x ^{2} + 3 x + 15}) = \frac{- 2 x ^{2} - 6 x + 21}{( x ^{2} + 3 x + 15 ) ^{2}}

= \frac{- 2 x ^{2} - 6 x + 21}{( x ^{2} + 3 x + 15 ) ^{2}}