d/(d{x)}(({z})(2{x}^2{y}+3{x}{z}+5{y}{z}^2-10))

解答

\frac{d}{d x} ((z) (2 x^{2} y + 3 x z + 5 y z^{2} - 10))

z (4 x y + 3 z)

求解步骤

\frac{d}{d x} ((z) (2 x^{2} y + 3 x z + 5 y z^{2} - 10))

将常数提出:

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

= z \frac{d}{d x} (2 x^{2} y + 3 x z + 5 y z^{2} - 10)

使用微分加减法定则:

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

= z (\frac{d}{d x} (2 x^{2} y) + \frac{d}{d x} (3 x z) + \frac{d}{d x} (5 y z^{2}) - \frac{d}{d x} (10))

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

\frac{d}{d x} (3 x z) = 3 z

\frac{d}{d x} (5 y z^{2}) = 0

\frac{d}{d x} (10) = 0

= z (4 x y + 3 z + 0 - 0)

化简

= z (4 x y + 3 z)

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