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

解

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

- \frac{324}{( 1 + 3 x ) ^{4}}

解答ステップ

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

\frac{d}{d x} (\frac{1 - 3 x}{1 + 3 x}) = - \frac{6}{( 1 + 3 x ) ^{2}}

= \frac{d ^{2}}{d x ^{2}} (- \frac{6}{( 1 + 3 x ) ^{2}})

\frac{d}{d x} (- \frac{6}{( 1 + 3 x ) ^{2}}) = \frac{36}{( 1 + 3 x ) ^{3}}

= \frac{d}{d x} (\frac{36}{( 1 + 3 x ) ^{3}})

\frac{d}{d x} (\frac{36}{( 1 + 3 x ) ^{3}}) = - \frac{324}{( 1 + 3 x ) ^{4}}

= - \frac{324}{( 1 + 3 x ) ^{4}}