derivative y= 5/((2x)^3)

解答

导数

y = \frac{5}{( 2 x ) ^{3}}

- \frac{15}{8 x ^{4}}

求解步骤

\frac{d}{d x} (\frac{5}{( 2 x ) ^{3}})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{1}{( 2 x ) ^{3}})

使用指数法则:

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

= 5 \frac{d}{d x} ((2 x)^{- 3})

使用连锁律:

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

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

\frac{d}{d x} (2 x) = 2

= 5 (- \frac{3}{( 2 x ) ^{4}} \cdot 2)

化简

5 (- \frac{3}{( 2 x ) ^{4}} \cdot 2) : - \frac{15}{8 x ^{4}}

= - \frac{15}{8 x ^{4}}

\int 1 - \frac{8}{x ^{3}} d x

\frac{d}{d x} (\frac{sin ( x )}{cos ( x ) + 1})

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

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

a re a y = 2 x, y = 2 x - 12, y = 0