(\partial)/(\partial x)(arcsin(11xyz))

解答

\frac{\partial}{\partial x} (arcsin (11 x yz))

\frac{11 yz}{1 - 121 x ^{2} y ^{2} z ^{2}}

求解步骤

\frac{\partial}{\partial x} (arcsin (11 x yz))

将

y, z

视为常数

使用连锁律:

\frac{1}{1 - ( 11 x yz ) ^{2}} \frac{\partial}{\partial x} (11 x yz)

= \frac{1}{1 - ( 11 x yz ) ^{2}} \frac{\partial}{\partial x} (11 x yz)

\frac{\partial}{\partial x} (11 x yz) = 11 yz

= \frac{1}{1 - ( 11 x yz ) ^{2}} \cdot 11 yz

化简

\frac{1}{1 - ( 11 x yz ) ^{2}} \cdot 11 yz : \frac{11 yz}{1 - 121 x ^{2} y ^{2} z ^{2}}

= \frac{11 yz}{1 - 121 x ^{2} y ^{2} z ^{2}}

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