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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

8 e^{x}

x \to \infty lim (2 x^{3} - 1)

\frac{d y}{d x} = \frac{( 1 + x y )}{1 + x}

\frac{x}{x + 9}

\int (e^{2 x} + 3)^{4} \cdot e^{2 x} d x

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