(\partial)/(\partial x)(ye^{3x})

解答

\frac{\partial}{\partial x} (y e^{3 x})

y e^{3 x} \cdot 3

求解步骤

\frac{\partial}{\partial x} (y e^{3 x})

将

y

视为常数

将常数提出:

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

= y \frac{\partial}{\partial x} (e^{3 x})

使用连锁律:

e^{3 x} \frac{\partial}{\partial x} (3 x)

= e^{3 x} \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= y e^{3 x} \cdot 3

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

\frac{\partial}{\partial x} (2)

t \cdot y^{^{'}} + 4 y = 8 t

y^{^{''}} + 3 y^{^{'}} - 4 y = e^{- 4 x} + x e^{- x}

\frac{\partial}{\partial x} (z^{x y^{2}})