derivative of (-7/(sqrt(x)))

解答

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

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

求解步骤

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

化简

\frac{- 7}{x} : - \frac{7}{x}

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

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

化简

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

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

t an g e n t f (x) = - x^{2} - x + 4, at x = - 1

y^{^{''}} + 5 y^{^{'}} + 6 y = - 10 t e^{2 t}

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

d er i v a t i v e ln (x + x^{2} - 3)

\int_{0}^{1} 2 π (2 - y) (8 y^{2}) d y