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

The answer to (\partial)/(\partial x)(arcsin(y/x)) is -y/(xsqrt(x^2-y^2))

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} ((3 - e^{- x})^{2})

5 π r^{2}

n = 1 \sum \infty \frac{5}{2 ^{n} + 1}

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

\int_{- \infty}^{- 1} e^{- 24 t} d t

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