d/(d{x)}(({z})({x}^2{y}^3+3{z}^2-15{x}{y}-6{x}{z}))

解答

\frac{d}{d x} ((z) (x^{2} y^{3} + 3 z^{2} - 15 x y - 6 x z))

z (2 y^{3} x - 15 y - 6 z)

求解步骤

\frac{d}{d x} ((z) (x^{2} y^{3} + 3 z^{2} - 15 x y - 6 x z))

将常数提出:

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

= z \frac{d}{d x} (x^{2} y^{3} + 3 z^{2} - 15 x y - 6 x z)

使用微分加减法定则:

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

= z (\frac{d}{d x} (x^{2} y^{3}) + \frac{d}{d x} (3 z^{2}) - \frac{d}{d x} (15 x y) - \frac{d}{d x} (6 x z))

\frac{d}{d x} (x^{2} y^{3}) = 2 x y^{3}

\frac{d}{d x} (3 z^{2}) = 0

\frac{d}{d x} (15 x y) = 15 y

\frac{d}{d x} (6 x z) = 6 z

= z (2 x y^{3} + 0 - 15 y - 6 z)

化简

= z (2 y^{3} x - 15 y - 6 z)

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