d/(d{x)}(({z})(4{z}^3+3{x}{z}^2-{x}{y}{z}-2{x}{y}^2+7))

解答

\frac{d}{d x} ((z) (4 z^{3} + 3 x z^{2} - x y z - 2 x y^{2} + 7))

z (3 z^{2} - y z - 2 y^{2})

求解步骤

\frac{d}{d x} ((z) (4 z^{3} + 3 x z^{2} - x y z - 2 x y^{2} + 7))

将常数提出:

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

= z \frac{d}{d x} (4 z^{3} + 3 x z^{2} - x y z - 2 x y^{2} + 7)

使用微分加减法定则:

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

= z (\frac{d}{d x} (4 z^{3}) + \frac{d}{d x} (3 x z^{2}) - \frac{d}{d x} (x y z) - \frac{d}{d x} (2 x y^{2}) + \frac{d}{d x} (7))

\frac{d}{d x} (4 z^{3}) = 0

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

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

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

\frac{d}{d x} (7) = 0

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

化简

= z (3 z^{2} - y z - 2 y^{2})

e x p an d \frac{3 x ^{2} + 2 x - 3}{( x ^{2} + 1 ) ^{2}}

e x p an d lo g_{6} (4 9 w)

e x p an d \frac{1}{( z + 1 ) ( z - 1 )}

e x p an d \frac{( x ^{2} + 5 x + 9 ) ^{n} + x ^{2} ( x + 5 ) ^{2} + 2}{x ^{2} + 5 x + 8}

e x p an d x ((x - 1) (x - 2))