(d^3)/(dx^3)(sqrt(6x+3))

解

\frac{d ^{3}}{d x ^{3}} (6 x + 3)

\frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

解答ステップ

\frac{d ^{3}}{d x ^{3}} (6 x + 3)

\frac{d}{d x} (6 x + 3) = \frac{3}{6 x + 3}

= \frac{d ^{2}}{d x ^{2}} (\frac{3}{6 x + 3})

\frac{d}{d x} (\frac{3}{6 x + 3}) = - \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}}

= \frac{d}{d x} (- \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}})

\frac{d}{d x} (- \frac{9}{( 6 x + 3 ) ^{\frac{3}{2}}}) = \frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}

= \frac{81}{( 6 x + 3 ) ^{\frac{5}{2}}}