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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int sin^{3} (11 x) cos^{2} (11 x) d x

\frac{d}{d x} ((1 + \frac{1}{x})^{x})

0.025 sin (\frac{2 π t}{10})

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

\int_{1}^{l n (8)} \int_{0}^{l n (y)} e^{x + y} d x d y

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