What is the derivative of y=xarcsin(x)+sqrt(1-x^2) ?

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

What is the first derivative of y=xarcsin(x)+sqrt(1-x^2) ?

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

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derivative of

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

arcsin (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= arcsin (x)

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