(\partial)/(\partial x)(2x^3+3y^3-12xy)

解答

\frac{\partial}{\partial x} (2 x^{3} + 3 y^{3} - 12 x y)

6 x^{2} - 12 y

求解步骤

\frac{\partial}{\partial x} (2 x^{3} + 3 y^{3} - 12 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^{3}) + \frac{\partial}{\partial x} (3 y^{3}) - \frac{\partial}{\partial x} (12 x y)

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

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

\frac{\partial}{\partial x} (12 x y) = 12 y

= 6 x^{2} + 0 - 12 y

化简

= 6 x^{2} - 12 y

\int \frac{1}{( x ^{2} - 6 x ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial x} (x y E (x, y) (x, y)^{\frac{x}{y}})

\int - 2 cos^{2} (x) d x

f (x) = 2 sec (3 x^{2})

(6 y + 2 t - 7) d t + (8 y + 6 t - 1) d y = 0, y (- 1) = 2