(\partial)/(\partial x)(2x^4+3y^3+2xy)

解答

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

8 x^{3} + 2 y

求解步骤

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

将

y

视为常数

使用微分加减法定则:

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

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

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

\frac{\partial}{\partial x} (3 y^{3}) = 0

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

= 8 x^{3} + 0 + 2 y

化简

= 8 x^{3} + 2 y

\int \frac{4 x ^{2} + 2 x - 1}{x ^{3} + x ^{2}} d x

\frac{d}{d x} (a - x)

\int 2 sin^{6} (x) cos (x) d x

\int \frac{( x ^{3} )}{x ^{2} + 9} d x

d er i v a t i v e x^{\frac{1}{3}} (x + 3)^{\frac{2}{3}}