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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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}

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

Simplify

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

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

6 t^{2} - t

f (x) = x^{2} tan (x)

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

\int_{1}^{4} \frac{4}{x ^{2} + 4 x + 4} d x

x \to 0 lim (- 2)

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