(d^2)/(dx^2)(sqrt(r)+\sqrt[8]{r})

解

\frac{d ^{2}}{d x ^{2}} (r (x) + 8 r (x))

\frac{16 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{5}{4}} + ( 8 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{7}{8}} 8 r - 7 \frac{d r}{d x} ^{2} ) r ^{\frac{7}{8}}}{64 r ^{\frac{11}{4}}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (r + 8 r)

\frac{d}{d x} (r + 8 r) = \frac{\frac{d r}{d x}}{2 r} + \frac{\frac{d r}{d x}}{8 r ^{\frac{7}{8}}}

= \frac{d}{d x} (\frac{\frac{d r}{d x}}{2 r} + \frac{\frac{d r}{d x}}{8 r ^{\frac{7}{8}}})

\frac{d}{d x} (\frac{\frac{d r}{d x}}{2 r} + \frac{\frac{d r}{d x}}{8 r ^{\frac{7}{8}}}) = \frac{16 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{5}{4}} + ( 8 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{7}{8}} 8 r - 7 \frac{d r}{d x} ^{2} ) r ^{\frac{7}{8}}}{64 r ^{\frac{11}{4}}}

= \frac{16 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{5}{4}} + ( 8 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{7}{8}} 8 r - 7 \frac{d r}{d x} ^{2} ) r ^{\frac{7}{8}}}{64 r ^{\frac{11}{4}}}