derivative f(x)=-6/((1+3x)^2)

解答

导数

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

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

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

- 6 (- \frac{2}{( 1 + 3 x ) ^{3}} \cdot 3) : \frac{36}{( 1 + 3 x ) ^{3}}

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

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

d er i v a t i v e \frac{3}{t ^{3}}

n = 0 \sum \infty \frac{x ^{2 n}}{n !}

\frac{d}{d x} (\frac{e ^{x}}{x cos ( x )})

(\frac{2 y}{x} + 2 x) + (2 ln (x) - 3) \frac{d y}{d x} = 0