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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x ^{3}}{( 5 - x ^{4} ) ^{6}} d x

\frac{d y}{d x} = - x y

\int_{0}^{2 π} cos^{2} (6 x) d x

\frac{\partial}{\partial x} (2 x^{3} + 3 y^{2} - 6 x y + 2)

\frac{d}{d x} ((2 x^{4} - x + 1) (- x^{5} + 4))

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