(\partial}{\partial x}(e^{\frac{-2y)/x})

解答

\frac{\partial}{\partial x} (e^{\frac{- 2 y}{x}})

\frac{2 e ^{- \frac{2 y}{x}} y}{x ^{2}}

求解步骤

\frac{\partial}{\partial x} (e^{\frac{- 2 y}{x}})

化简

e^{\frac{- 2 y}{x}} : e^{- \frac{2 y}{x}}

= \frac{\partial}{\partial x} (e^{- \frac{2 y}{x}})

将

y

视为常数

使用连锁律:

e^{- \frac{2 y}{x}} \frac{\partial}{\partial x} (- \frac{2 y}{x})

= e^{- \frac{2 y}{x}} \frac{\partial}{\partial x} (- \frac{2 y}{x})

\frac{\partial}{\partial x} (- \frac{2 y}{x}) = \frac{2 y}{x ^{2}}

= e^{- \frac{2 y}{x}} \frac{2 y}{x ^{2}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 e ^{- \frac{2 y}{x}} y}{x ^{2}}

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{4}})

g (f) = f^{8}

\int \frac{1}{x + 5} d x

l a pl a ce t r an s f or m e^{- 3 t} + 3

\int \frac{- t}{( t + 1 ) - ( t + 1 )} d t