(d^2)/(dx^2)(sqrt(r)+\sqrt[7]{r})

解

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

\frac{49 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{17}{14}} + 4 ( 7 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{6}{7}} 7 r - 6 \frac{d r}{d x} ^{2} ) r ^{\frac{6}{7}}}{196 r ^{\frac{19}{7}}}

解答ステップ

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

\frac{d}{d x} (r + 7 r) = \frac{\frac{d r}{d x}}{2 r} + \frac{\frac{d r}{d x}}{7 r ^{\frac{6}{7}}}

= \frac{d}{d x} (\frac{\frac{d r}{d x}}{2 r} + \frac{\frac{d r}{d x}}{7 r ^{\frac{6}{7}}})

\frac{d}{d x} (\frac{\frac{d r}{d x}}{2 r} + \frac{\frac{d r}{d x}}{7 r ^{\frac{6}{7}}}) = \frac{49 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{17}{14}} + 4 ( 7 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{6}{7}} 7 r - 6 \frac{d r}{d x} ^{2} ) r ^{\frac{6}{7}}}{196 r ^{\frac{19}{7}}}

= \frac{49 ( 2 \frac{d ^{2} r}{d x ^{2}} r - \frac{d r}{d x} ^{2} ) r ^{\frac{17}{14}} + 4 ( 7 \frac{d ^{2} r}{d x ^{2}} r ^{\frac{6}{7}} 7 r - 6 \frac{d r}{d x} ^{2} ) r ^{\frac{6}{7}}}{196 r ^{\frac{19}{7}}}