derivative of 8/(sqrt(x^2+6x))

解答

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

- \frac{4 ( 2 x + 6 )}{( x ^{2} + 6 x ) ^{\frac{3}{2}}}

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

8 (- \frac{1}{2 ( x ^{2} + 6 x ) ^{\frac{3}{2}}} (2 x + 6)) : - \frac{4 ( 2 x + 6 )}{( x ^{2} + 6 x ) ^{\frac{3}{2}}}

= - \frac{4 ( 2 x + 6 )}{( x ^{2} + 6 x ) ^{\frac{3}{2}}}