(\partial)/(\partial x)(2x^3+6xy-2y^4)

解答

\frac{\partial}{\partial x} (2 x^{3} + 6 x y - 2 y^{4})

6 x^{2} + 6 y

求解步骤

\frac{\partial}{\partial x} (2 x^{3} + 6 x y - 2 y^{4})

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^{3}) + \frac{\partial}{\partial x} (6 x y) - \frac{\partial}{\partial x} (2 y^{4})

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (2 y^{4}) = 0

= 6 x^{2} + 6 y - 0

化简

= 6 x^{2} + 6 y

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

\int \frac{2 x}{4 - x ^{4}} d x

\int \frac{x + 4}{x ^{3}} d x

f (x) = 2 x - 1

\int (4 x^{7} - 3 cos (x)) d x