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

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

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(\partial)/(\partial y)(arcsin(xy))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{x ^{2} - 4 x + 9} d x

f (x) = 6 x - x^{2}, at x = 1

z \to 0 lim (\frac{- 1}{z})

\int \frac{x ^{3}}{x ^{4} - 7} d x

\frac{d}{d x} (⌊ \frac{3}{2} ⌋)

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