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

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

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(\partial)/(\partial x)(xarcsin(x)y)

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arcsin (x)

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

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

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

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

Simplify

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

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

\int_{0}^{\frac{π}{2}} x sin (4 x) d x

x \to 5 - lim (\frac{5}{( x - 5 ) ^{3}})

4 x

\int 3 + s (s + 1)^{2} d s

f (x) = ln (25 sin^{2} (x))

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