derivative of (sqrt(3)/(2sqrt(x)))

解答

\frac{d}{d x} (\frac{3}{2 x})

- \frac{3}{4 x ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{3}{2 x})

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

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

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

化简

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

= - \frac{3}{4 x ^{\frac{3}{2}}}

\frac{\partial}{\partial y} (3 + x ln (x y - 7))

d er i v a t i v e f (x) = 1 + x^{2}

\frac{\partial}{\partial x} (5 arctan (x))

x \to + (- 2) lim (lo g_{2} (8))

\int e^{- x + 1} d x