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

解答

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

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

求解步骤

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

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

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

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

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

e x p an d 5 (1 - e^{\frac{10}{t}})

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e x p an d \frac{x ^{9} y - x ^{9}}{( x ^{6} + y ^{2} - 2 y + 1 ) ^{2}}