d/(ds)(4^{-3}(2/(s^7)+3s)^4)

解答

\frac{d}{d s} (4^{- 3} (\frac{2}{s ^{7}} + 3 s)^{4})

\frac{( - 14 + 3 s ^{8} ) ( 2 + 3 s ^{8} ) ^{3}}{16 s ^{29}}

求解步骤

\frac{d}{d s} (4^{- 3} (\frac{2}{s ^{7}} + 3 s)^{4})

将常数提出:

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

= 4^{- 3} \frac{d}{d s} ((\frac{2}{s ^{7}} + 3 s)^{4})

使用连锁律:

4 (\frac{2}{s ^{7}} + 3 s)^{3} \frac{d}{d s} (\frac{2}{s ^{7}} + 3 s)

= 4 (\frac{2}{s ^{7}} + 3 s)^{3} \frac{d}{d s} (\frac{2}{s ^{7}} + 3 s)

\frac{d}{d s} (\frac{2}{s ^{7}} + 3 s) = - \frac{14}{s ^{8}} + 3

= 4^{- 3} \cdot 4 (\frac{2}{s ^{7}} + 3 s)^{3} (- \frac{14}{s ^{8}} + 3)

化简

4^{- 3} \cdot 4 (\frac{2}{s ^{7}} + 3 s)^{3} (- \frac{14}{s ^{8}} + 3) : \frac{( - 14 + 3 s ^{8} ) ( 2 + 3 s ^{8} ) ^{3}}{16 s ^{29}}

= \frac{( - 14 + 3 s ^{8} ) ( 2 + 3 s ^{8} ) ^{3}}{16 s ^{29}}

\int x^{3} ln ∣ 1 + x ∣ d x

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

d er i v a t i v e f (x) = \frac{x ^{3} + 2 x ^{2} + 3 x + 4}{x}

\frac{d}{d x} (9 - x)

d er i v a t i v e 4 π x^{2}