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}} (- 1))

化简

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

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

x \to 0 lim (x - tan (x))

d er i v a t i v e f (x) = \frac{x}{6 + x}

d er i v a t i v e f (x) = x in x

\int \frac{1}{1 - x ^{2}} x d x

\frac{d}{d x} (c e^{\frac{y}{x}})