derivative of 6/((1+x^4))

解答

\frac{d}{d x} (\frac{6}{( 1 + x ) ^{4}})

- \frac{24}{( 1 + x ) ^{5}}

求解步骤

\frac{d}{d x} (\frac{6}{( 1 + x ) ^{4}})

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

- \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

= - \frac{4}{( 1 + x ) ^{5}} \frac{d}{d x} (1 + x)

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

= 6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1)

化简

6 (- \frac{4}{( 1 + x ) ^{5}} \cdot 1) : - \frac{24}{( 1 + x ) ^{5}}

= - \frac{24}{( 1 + x ) ^{5}}

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

t an g e n t f (x) = x^{2} + x

\int sec (5 x) tan (5 x) d x

\frac{d}{d x} (sec (\frac{1}{x}))

x \to 1 lim (- 1)