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

The derivative of x/(1+sqrt(1-x^2)) is 1/((sqrt(-x^2+1)+1)\sqrt{-x^2+1)}

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

The first derivative of x/(1+sqrt(1-x^2)) is 1/((sqrt(-x^2+1)+1)\sqrt{-x^2+1)}

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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