(\partial)/(\partial x)(x*e^{x^3y})

解答

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

e^{x^{3} y} + 3 e^{x^{3} y} x^{3} y

求解步骤

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

将

y

视为常数

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x^{3} y}

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

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

\frac{\partial}{\partial x} (e^{x^{3} y}) = e^{x^{3} y} \cdot 3 y x^{2}

= 1 \cdot e^{x^{3} y} + e^{x^{3} y} \cdot 3 y x^{2} x

化简

1 \cdot e^{x^{3} y} + e^{x^{3} y} \cdot 3 y x^{2} x : e^{x^{3} y} + 3 e^{x^{3} y} x^{3} y

= e^{x^{3} y} + 3 e^{x^{3} y} x^{3} y

y d y + (1 + y^{2}) sin (t) d t = 0

\frac{d}{d x} (e x)

t an g e n t y = 1 + x

\int 14 tan^{3} (x) sec (x) d x

x \to 0 + lim (x^{x^{\frac{1}{2}}})