What is (\partial)/(\partial x)(arcsin(2xyz)) ?

The answer to (\partial)/(\partial x)(arcsin(2xyz)) is (2yz)/(sqrt(1-4x^2y^2z^2))

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(\partial)/(\partial x)(arcsin(2xyz))

\frac{\partial}{\partial x} (arcsin (2 x yz))

\frac{2 yz}{1 - 4 x ^{2} y ^{2} z ^{2}}

Solution steps

\frac{\partial}{\partial x} (arcsin (2 x yz))

Treat

y, z

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 x yz) = 2 yz

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

Simplify

\frac{1}{1 - ( 2 x yz ) ^{2}} \cdot 2 yz : \frac{2 yz}{1 - 4 x ^{2} y ^{2} z ^{2}}

= \frac{2 yz}{1 - 4 x ^{2} y ^{2} z ^{2}}

What is (\partial)/(\partial x)(arcsin(2xyz)) ?
The answer to (\partial)/(\partial x)(arcsin(2xyz)) is (2yz)/(sqrt(1-4x^2y^2z^2))