(\partial)/(\partial y)(2x^{1/2}y^{1/4}+7)

解答

\frac{\partial}{\partial y} (2 x^{\frac{1}{2}} y^{\frac{1}{4}} + 7)

\frac{x ^{\frac{1}{2}}}{2 y ^{\frac{3}{4}}}

求解步骤

\frac{\partial}{\partial y} (2 x^{\frac{1}{2}} y^{\frac{1}{4}} + 7)

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^{\frac{1}{2}} y^{\frac{1}{4}}) + \frac{\partial}{\partial y} (7)

\frac{\partial}{\partial y} (2 x^{\frac{1}{2}} y^{\frac{1}{4}}) = \frac{x ^{\frac{1}{2}}}{2 y ^{\frac{3}{4}}}

\frac{\partial}{\partial y} (7) = 0

= \frac{x ^{\frac{1}{2}}}{2 y ^{\frac{3}{4}}} + 0

化简

= \frac{x ^{\frac{1}{2}}}{2 y ^{\frac{3}{4}}}

\int \frac{7 x ^{2} + x + 7}{( x ^{2} + 1 ) ^{2}} d x

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

t an g e n t f (x) = 4 x - 3 x, (4, 10)

\frac{d}{d x} (e^{x + l n (x)})

x \to \infty lim ((- 2)^{x})