(d^2)/(dh^2)(({V}(h))((3h^2+4)^{3/2}-8))

解

\frac{d ^{2}}{d h ^{2}} ((V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8))

\frac{54 h ^{3} \frac{d}{d h} ( V ( h ) ) + 54 h ^{2} V ( h ) + 72 h \frac{d}{d h} ( V ( h ) ) + 36 V ( h ) + \frac{d ^{2}}{d h ^{2}} ( V ( h ) ) ( 3 h ^{2} + 4 ) ^{2} - 8 \frac{d ^{2}}{d h ^{2}} ( V ( h ) ) ( 3 h ^{2} + 4 ) ^{\frac{1}{2}}}{( 3 h ^{2} + 4 ) ^{\frac{1}{2}}}

解答ステップ

\frac{d ^{2}}{d h ^{2}} ((V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8))

\frac{d}{d h} (V (h) ((3 h^{2} + 4)^{\frac{3}{2}} - 8)) = \frac{d}{d h} (V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8) + 9 h (3 h^{2} + 4)^{\frac{1}{2}} V (h)

= \frac{d}{d h} (\frac{d}{d h} (V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8) + 9 h (3 h^{2} + 4)^{\frac{1}{2}} V (h))

\frac{d}{d h} (\frac{d}{d h} (V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8) + 9 h (3 h^{2} + 4)^{\frac{1}{2}} V (h)) = \frac{54 h ^{3} \frac{d}{d h} ( V ( h ) ) + 54 h ^{2} V ( h ) + 72 h \frac{d}{d h} ( V ( h ) ) + 36 V ( h ) + \frac{d ^{2}}{d h ^{2}} ( V ( h ) ) ( 3 h ^{2} + 4 ) ^{2} - 8 \frac{d ^{2}}{d h ^{2}} ( V ( h ) ) ( 3 h ^{2} + 4 ) ^{\frac{1}{2}}}{( 3 h ^{2} + 4 ) ^{\frac{1}{2}}}

= \frac{54 h ^{3} \frac{d}{d h} ( V ( h ) ) + 54 h ^{2} V ( h ) + 72 h \frac{d}{d h} ( V ( h ) ) + 36 V ( h ) + \frac{d ^{2}}{d h ^{2}} ( V ( h ) ) ( 3 h ^{2} + 4 ) ^{2} - 8 \frac{d ^{2}}{d h ^{2}} ( V ( h ) ) ( 3 h ^{2} + 4 ) ^{\frac{1}{2}}}{( 3 h ^{2} + 4 ) ^{\frac{1}{2}}}