(\partial)/(\partial y)(3.25yzcos(xyz))

解答

\frac{\partial}{\partial y} (3.25 yz cos (x yz))

3.25 z (cos (yz x) - yz x sin (yz x))

求解步骤

\frac{\partial}{\partial y} (3.25 yz cos (x yz))

将

z, x

视为常数

将常数提出:

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

= 3.25 z \frac{\partial}{\partial y} (y cos (x yz))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = cos (x yz)

= 3.25 z (\frac{\partial}{\partial y} (y) cos (x yz) + \frac{\partial}{\partial y} (cos (x yz)) y)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (cos (x yz)) = - sin (x yz) z x

= 3.25 z (1 \cdot cos (x yz) + (- sin (x yz) z x) y)

化简

= 3.25 z (cos (yz x) - yz x sin (yz x))

\frac{d}{d x} (x^{\frac{1}{3}} (x^{2} - 4))

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