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

The derivative of sqrt(((1-x)/(1+x))) is -1/(sqrt(-x+1)(x+1)^{3/2)}

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

The first derivative of sqrt(((1-x)/(1+x))) is -1/(sqrt(-x+1)(x+1)^{3/2)}

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

- \frac{1}{- x + 1 ( x + 1 ) ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 \frac{1 - x}{1 + x}} (- \frac{2}{( 1 + x ) ^{2}}) : - \frac{1}{- x + 1 ( x + 1 ) ^{\frac{3}{2}}}

= - \frac{1}{- x + 1 ( x + 1 ) ^{\frac{3}{2}}}

What is the derivative of sqrt(((1-x)/(1+x))) ?
The derivative of sqrt(((1-x)/(1+x))) is -1/(sqrt(-x+1)(x+1)^{3/2)}
What is the first derivative of sqrt(((1-x)/(1+x))) ?
The first derivative of sqrt(((1-x)/(1+x))) is -1/(sqrt(-x+1)(x+1)^{3/2)}