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

解答

导数

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

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用指数法则:

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

= - 3 \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

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

化简

- 3 (- \frac{2}{( 3 x + 1 ) ^{3}} \cdot 3) : \frac{18}{( 3 x + 1 ) ^{3}}

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

\frac{d y}{d x} = \frac{x ^{2} + y ^{2}}{2 y}

x \to 3 lim (\frac{1}{x} - \frac{1}{3})

(y x^{2} - y) d y = tan^{- 1} (x) d x

\int \frac{1}{sec ^{3} ( x )} d x

l a pl a ce t r an s f or m e^{- t} + e^{- 2 t}