(d^4)/(dx^4)(1/(3x+1))

解

\frac{d ^{4}}{d x ^{4}} (\frac{1}{3 x + 1})

\frac{1944}{( 3 x + 1 ) ^{5}}

解答ステップ

\frac{d ^{4}}{d x ^{4}} (\frac{1}{3 x + 1})

\frac{d}{d x} (\frac{1}{3 x + 1}) = - \frac{3}{( 3 x + 1 ) ^{2}}

= \frac{d ^{3}}{d x ^{3}} (- \frac{3}{( 3 x + 1 ) ^{2}})

\frac{d}{d x} (- \frac{3}{( 3 x + 1 ) ^{2}}) = \frac{18}{( 3 x + 1 ) ^{3}}

= \frac{d ^{2}}{d x ^{2}} (\frac{18}{( 3 x + 1 ) ^{3}})

\frac{d}{d x} (\frac{18}{( 3 x + 1 ) ^{3}}) = - \frac{162}{( 3 x + 1 ) ^{4}}

= \frac{d}{d x} (- \frac{162}{( 3 x + 1 ) ^{4}})

\frac{d}{d x} (- \frac{162}{( 3 x + 1 ) ^{4}}) = \frac{1944}{( 3 x + 1 ) ^{5}}

= \frac{1944}{( 3 x + 1 ) ^{5}}