derivative (64)/((1+4x)^3)

解答

导数

\frac{64}{( 1 + 4 x ) ^{3}}

- \frac{768}{( 1 + 4 x ) ^{4}}

求解步骤

\frac{d}{d x} (\frac{64}{( 1 + 4 x ) ^{3}})

将常数提出:

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

= 64 \frac{d}{d x} (\frac{1}{( 1 + 4 x ) ^{3}})

使用指数法则:

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

= 64 \frac{d}{d x} ((1 + 4 x)^{- 3})

使用连锁律:

- \frac{3}{( 1 + 4 x ) ^{4}} \frac{d}{d x} (1 + 4 x)

= - \frac{3}{( 1 + 4 x ) ^{4}} \frac{d}{d x} (1 + 4 x)

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

= 64 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4)

化简

64 (- \frac{3}{( 1 + 4 x ) ^{4}} \cdot 4) : - \frac{768}{( 1 + 4 x ) ^{4}}

= - \frac{768}{( 1 + 4 x ) ^{4}}

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

x \to 9 lim (8 x + ∣ x - 9 ∣)

\frac{\partial}{\partial y} (2 x y^{3} - 3)

d er i v a t i v e 4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 3 x

y^{^{'}} = \frac{( y - y ^{2} )}{x}