derivative of ((x^2+2/(x^3-1))^3)

解答

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

\frac{3 ( x ^{2} + 2 ) ^{2} ( - x ^{4} - 6 x ^{2} - 2 x )}{( x ^{3} - 1 ) ^{4}}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{3} - 1}) = \frac{- x ^{4} - 6 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}}

= 3 (\frac{x ^{2} + 2}{x ^{3} - 1})^{2} \frac{- x ^{4} - 6 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}}

化简

3 (\frac{x ^{2} + 2}{x ^{3} - 1})^{2} \frac{- x ^{4} - 6 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}} : \frac{3 ( x ^{2} + 2 ) ^{2} ( - x ^{4} - 6 x ^{2} - 2 x )}{( x ^{3} - 1 ) ^{4}}

= \frac{3 ( x ^{2} + 2 ) ^{2} ( - x ^{4} - 6 x ^{2} - 2 x )}{( x ^{3} - 1 ) ^{4}}

in v erse l a pl a ce \frac{1}{s ^{3} ( s ^{2} + 1 )}

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

\int e^{- 21 x} d x

\int \frac{1}{x ^{4} - x ^{3}} d x

l a pl a ce t r an s f or m cos (3 x)