(\partial)/(\partial y)((x)(x^3yz^2+2yz))

解答

\frac{\partial}{\partial y} ((x) (x^{3} y z^{2} + 2 yz))

x (x^{3} z^{2} + 2 z)

求解步骤

\frac{\partial}{\partial y} ((x) (x^{3} y z^{2} + 2 yz))

将

x, z

视为常数

将常数提出:

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

= x \frac{\partial}{\partial y} (x^{3} y z^{2} + 2 yz)

使用微分加减法定则:

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

= x (\frac{\partial}{\partial y} (x^{3} y z^{2}) + \frac{\partial}{\partial y} (2 yz))

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

\frac{\partial}{\partial y} (2 yz) = 2 z

= x (x^{3} z^{2} + 2 z)

e x p an d x \cdot (1 + x + 1 - x)

e x p an d \frac{1}{4} (e^{2 x} \cdot 2 x - e^{2 x}) + C

e x p an d \frac{27 \times ( s + 2 )}{2}

s im pl i f y (2 + 4 i)^{4}

s im pl i f y (y - x^{2}) (\frac{2 y ( y - x ^{2} )}{y ^{2} - x} - 1)