(\partial)/(\partial x)(x^3y^7)

解答

\frac{\partial}{\partial x} (x^{3} y^{7})

3 x^{2} y^{7}

求解步骤

\frac{\partial}{\partial x} (x^{3} y^{7})

将

y

视为常数

将常数提出:

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

= y^{7} \frac{\partial}{\partial x} (x^{3})

使用幂法则:

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

= y^{7} \cdot 3 x^{3 - 1}

化简

= 3 x^{2} y^{7}

l a pl a ce t r an s f or m - 5 t^{2} e^{- 4 t} + sin (3 t)

\frac{d}{d x} (x^{3} - 7 x^{2} + 14 x - 6)

\frac{\partial}{\partial u} (\frac{u}{v + 1})

\int g e^{- 2 c t} d t

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