What is (\partial)/(\partial x)(arcsin(x/(y^2))) ?

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

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(\partial)/(\partial x)(arcsin(x/(y^2)))

\frac{\partial}{\partial x} (arcsin (\frac{x}{y ^{2}}))

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

Solution steps

\frac{\partial}{\partial x} (arcsin (\frac{x}{y ^{2}}))

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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