derivative of 1/(sqrt(7x))

解答

\frac{d}{d x} (\frac{1}{7 x})

- \frac{1}{2 7 x ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{1}{7 x})

使用指数法则:

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

= \frac{d}{d x} ((7 x)^{- \frac{1}{2}})

使用连锁律:

- \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x)

= - \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= - \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \cdot 7

化简

- \frac{1}{2 ( 7 x ) ^{\frac{3}{2}}} \cdot 7 : - \frac{1}{2 7 x ^{\frac{3}{2}}}

= - \frac{1}{2 7 x ^{\frac{3}{2}}}

\int (x^{2} - 1) (2 x + 1) d x

\int cos^{6} (2 x) d x

(y + 1) y^{^{'}} = x y - y

\frac{d y}{d x} = e^{2 y + 8 x}

\frac{d}{d x} (sin^{3} (x^{2} + 7))