(\partial)/(\partial x)(2x^2-4xy+xyz)

解答

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

4 x - 4 y + yz

求解步骤

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

将

y, z

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

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

\frac{\partial}{\partial x} (4 x y) = 4 y

\frac{\partial}{\partial x} (x yz) = yz

= 4 x - 4 y + yz

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

x^{4} e^{y} + (x + 1) y \frac{d y}{d x} = 0

d er i v a t i v e f (x) = (1 + cos^{2} (x))^{6}

\int_{5}^{10} a x - 10 b d x

t an g e n t f (x) = \frac{12}{x}, at x = - 2