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

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

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(\partial)/(\partial x)(arcsin(xy))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\frac{\partial}{\partial y} (15 - 5 (y + 3)^{2})

\frac{\partial}{\partial x} (7 x^{3} cos (7 x^{2} y))

\frac{\partial}{\partial y} (3 x^{4} y^{2} + 1)

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