(d^2)/(dx^2)(sqrt(r)+\sqrt[3]{r})

解

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

\frac{9 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{5}{6}} + 4 ( 3 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{2}{3}} 3 r - 2 \frac{d r}{d x} ^{2} ) r ^{\frac{2}{3}}}{36 r ^{\frac{7}{3}}}

解答ステップ

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

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

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

\frac{d}{d x} (\frac{\frac{d r}{d x}}{2 r} + \frac{\frac{d r}{d x}}{3 r ^{\frac{2}{3}}}) = \frac{9 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{5}{6}} + 4 ( 3 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{2}{3}} 3 r - 2 \frac{d r}{d x} ^{2} ) r ^{\frac{2}{3}}}{36 r ^{\frac{7}{3}}}

= \frac{9 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{5}{6}} + 4 ( 3 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{2}{3}} 3 r - 2 \frac{d r}{d x} ^{2} ) r ^{\frac{2}{3}}}{36 r ^{\frac{7}{3}}}