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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

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