What is the derivative of x^2arcsin(x) ?

The derivative of x^2arcsin(x) is 2xarcsin(x)+(x^2)/(sqrt(1-x^2))

What is the first derivative of x^2arcsin(x) ?

The first derivative of x^2arcsin(x) is 2xarcsin(x)+(x^2)/(sqrt(1-x^2))

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = arcsin (x)

= \frac{d}{d x} (x^{2}) arcsin (x) + \frac{d}{d x} (arcsin (x)) x^{2}

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

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

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

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

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

What is the derivative of x^2arcsin(x) ?
The derivative of x^2arcsin(x) is 2xarcsin(x)+(x^2)/(sqrt(1-x^2))
What is the first derivative of x^2arcsin(x) ?
The first derivative of x^2arcsin(x) is 2xarcsin(x)+(x^2)/(sqrt(1-x^2))