(\partial)/(\partial x)(-1/2 ln(x/a))

解答

\frac{\partial}{\partial x} (- \frac{1}{2} ln (\frac{x}{a}))

- \frac{1}{2 x}

求解步骤

\frac{\partial}{\partial x} (- \frac{1}{2} ln (\frac{x}{a}))

将常数提出:

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

= - \frac{1}{2} \frac{\partial}{\partial x} (ln (\frac{x}{a}))

使用连锁律:

\frac{1}{\frac{x}{a}} \frac{\partial}{\partial x} (\frac{x}{a})

= \frac{1}{\frac{x}{a}} \frac{\partial}{\partial x} (\frac{x}{a})

\frac{\partial}{\partial x} (\frac{x}{a}) = \frac{1}{a}

= - \frac{1}{2} \cdot \frac{1}{\frac{x}{a}} \cdot \frac{1}{a}

化简

- \frac{1}{2} \cdot \frac{1}{\frac{x}{a}} \cdot \frac{1}{a} : - \frac{1}{2 x}

= - \frac{1}{2 x}

t an g e n t f (x) = x (x - 8), at x = 16

\int_{0}^{3} 6 y - 2 y^{2} d y

t a y l or ln (2 + x)

d er i v a t i v e - x + tan (x)

d er i v a t i v e cos (\frac{1 - e ^{7 x}}{1 + e ^{7 x}})