d/(d{x)}(({z})({x}+2{y}+{z}-2sqrt({x){y}{z}}))

解答

\frac{d}{d x} ((z) (x + 2 y + z - 2 x y z))

z (\frac{d}{d x} (z) + 1 - \frac{y z}{x})

求解步骤

\frac{d}{d x} ((z) (x + 2 y + z - 2 x y z))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{d}{d x} (x + 2 y + z - 2 x y z)

使用微分加减法定则:

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

= z (\frac{d}{d x} (x) + \frac{d}{d x} (2 y) + \frac{d}{d x} (z) - \frac{d}{d x} (2 x y z))

\frac{d}{d x} (x) = 1

\frac{d}{d x} (2 y) = 0

\frac{d}{d x} (2 x y z) = \frac{y z}{x}

= z (1 + 0 + \frac{d}{d x} (z) - \frac{y z}{x})

化简

= z (\frac{d}{d x} (z) + 1 - \frac{y z}{x})

e x p an d (2 e + 4)^{2}

e x p an d \frac{( x + 4 ) 3}{4}

e x p an d (\frac{x}{y} + ln (x) + sin (y)) d y

e x p an d csc (x) cos (x) sin (x)

e x p an d (135 + y) tan (2 1^{\circ})