derivative of (1/(3x+1)^4)

解答

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

- \frac{12}{( 3 x + 1 ) ^{5}}

求解步骤

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

使用连锁律:

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

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

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

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

化简

4 (\frac{1}{3 x + 1})^{3} (- \frac{3}{( 3 x + 1 ) ^{2}}) : - \frac{12}{( 3 x + 1 ) ^{5}}

= - \frac{12}{( 3 x + 1 ) ^{5}}

in v erse l a pl a ce \frac{4}{s ^{2} + 9}

\int 11 sin^{5} (x) d x

\int \frac{x ^{2}}{2 - x ^{3}} d x

d er i v a t i v e y = 3 e^{- x} + e^{4 x}

\int x x d x