What is (\partial)/(\partial x)(xarcsin(3x)) ?

The answer to (\partial)/(\partial x)(xarcsin(3x)) is arcsin(3x)+(3x)/(sqrt(1-9x^2))

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(\partial)/(\partial x)(xarcsin(3x))

\frac{\partial}{\partial x} (x arcsin (3 x))

arcsin (3 x) + \frac{3 x}{1 - 9 x ^{2}}

Solution steps

\frac{\partial}{\partial x} (x arcsin (3 x))

Apply the Product Rule:

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

f = x, g = arcsin (3 x)

= \frac{\partial}{\partial x} (x) arcsin (3 x) + \frac{\partial}{\partial x} (arcsin (3 x)) x

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

\frac{\partial}{\partial x} (arcsin (3 x)) = \frac{3}{1 - 9 x ^{2}}

= 1 \cdot arcsin (3 x) + \frac{3}{1 - 9 x ^{2}} x

Simplify

1 \cdot arcsin (3 x) + \frac{3}{1 - 9 x ^{2}} x : arcsin (3 x) + \frac{3 x}{1 - 9 x ^{2}}

= arcsin (3 x) + \frac{3 x}{1 - 9 x ^{2}}

f (x) = sin (4 x^{2})

x \to 0 lim (\frac{cos ( 2 x )}{sin ( 2 x )})

f (x) = x^{3} - 3 x^{2} + 2 x - 2, at x = 2

\frac{2}{r ^{3}}

x \to 0 lim (\frac{1}{ln ( x )})

What is (\partial)/(\partial x)(xarcsin(3x)) ?
The answer to (\partial)/(\partial x)(xarcsin(3x)) is arcsin(3x)+(3x)/(sqrt(1-9x^2))