What is the derivative of xarcsin(x) ?

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

What is the first derivative of xarcsin(x) ?

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

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derivative of

x arcsin (x)

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = arcsin (x)

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

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

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

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

Simplify

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

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

n = 1 \sum \infty n!^{2} (5^{n})

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

x^{2} e^{- x} + (ln (x))^{2}

\int 3 s h^{3} x d x

\frac{70}{t}

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