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

解答

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

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

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用连锁律:

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

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

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

= x^{2} e^{- 2 y} (- 2)

化简

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

im pl i c i t \frac{d y}{d x}, y = x^{π}

a re a y = 3 x, y = \frac{1}{x}, x = 27

t y^{^{'}} + t^{2} + t y - y = 0

h \to 0 lim (\frac{( 1 + h ) ^{9} - 1}{h})

5 x y (\frac{d y}{d x}) = 3