(\partial)/(\partial y)(2xy^4+2)

解答

\frac{\partial}{\partial y} (2 x y^{4} + 2)

8 x y^{3}

求解步骤

\frac{\partial}{\partial y} (2 x y^{4} + 2)

将

x

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (2 x y^{4}) + \frac{\partial}{\partial y} (2)

\frac{\partial}{\partial y} (2 x y^{4}) = 8 x y^{3}

\frac{\partial}{\partial y} (2) = 0

= 8 x y^{3} + 0

化简

= 8 x y^{3}

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

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

\int_{\frac{1}{2}}^{1} \frac{4 y + 5}{y ^{2} + y} d y

\int_{- 5}^{5} \frac{1}{x ^{(\frac{2}{3})}} d x

d er i v a t i v e \frac{1}{3}