(\partial)/(\partial x)((8y)/(x^5))

解答

\frac{\partial}{\partial x} (\frac{8 y}{x ^{5}})

- \frac{40 y}{x ^{6}}

求解步骤

\frac{\partial}{\partial x} (\frac{8 y}{x ^{5}})

将

y

视为常数

将常数提出:

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

= 8 y \frac{\partial}{\partial x} (\frac{1}{x ^{5}})

使用指数法则:

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

= 8 y \frac{\partial}{\partial x} (x^{- 5})

使用幂法则:

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

= 8 y (- 5 x^{- 5 - 1})

化简

8 y (- 5 x^{- 5 - 1}) : - \frac{40 y}{x ^{6}}

= - \frac{40 y}{x ^{6}}

f (x) = \frac{1}{2 x + 1}

t an g e n t f (x) = \frac{2 x - 4}{x}, at x = 4

\frac{\partial}{\partial x} (\frac{t}{a ^{2} t ^{2} - x ^{2}})

\frac{d y}{d x} = 2 x y^{2} + 128 x

\frac{d y}{d x} = \frac{1}{2} (y - 1)^{2}, y (0) = 2