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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

Simplify

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

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

x \to 8 - lim (\frac{64 - x ^{2}}{x - 8})

\frac{d}{d x} (x 64 - x^{2})

\int_{0}^{5} π (25 - x^{2}) d x

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