derivative f(x)= 2/(sqrt(6+8x))

解答

导数

f (x) = \frac{2}{6 + 8 x}

- \frac{8}{( 6 + 8 x ) ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{2}{6 + 8 x})

将常数提出:

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

= 2 \frac{d}{d x} (\frac{1}{6 + 8 x})

使用指数法则:

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

= 2 \frac{d}{d x} ((6 + 8 x)^{- \frac{1}{2}})

使用连锁律:

- \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 + 8 x)

= - \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \frac{d}{d x} (6 + 8 x)

\frac{d}{d x} (6 + 8 x) = 8

= 2 (- \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \cdot 8)

化简

2 (- \frac{1}{2 ( 6 + 8 x ) ^{\frac{3}{2}}} \cdot 8) : - \frac{8}{( 6 + 8 x ) ^{\frac{3}{2}}}

= - \frac{8}{( 6 + 8 x ) ^{\frac{3}{2}}}

\frac{\partial}{\partial u} (2 u)

\int_{- 2}^{2} 16 - 4 y^{2} d y

x \to 0 + lim (ln (x) - \frac{1}{x})

x^{2} \frac{d y}{d x} + y^{2} = 0

\frac{d}{d x} (x^{3} + 7 x - 1)