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

解答

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

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

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

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

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

化简

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

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

f^{^{'}} (x) = (3 x^{5} - 2)^{20}

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

\int_{1}^{R} \frac{ln ( 4 x )}{x ^{2}} d x

\int \frac{e}{π} d x

d er i v a t i v e I n (x^{2})