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

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

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(\partial)/(\partial x)(arccos(y/x))

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

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

Solution steps

\frac{\partial}{\partial x} (arccos (\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}}

y^{^{'}} x^{2} - 18 = 4 x

\frac{d}{d x} (\frac{( 6 x ^{2} + 2 x + 8 )}{x})

\int_{0}^{1} \frac{30}{6 x ^{2} + 7 x + 1} d x

\int (6 x^{2} - 5 x + 3) d x

2 + 6 e^{a x}

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