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Popular Calculus >

derivative of sqrt((1-x)/(1+x))

Solution

derivative of

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

Solution

- \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}}}

Graph

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x \to 2 lim (\frac{2 ^{x} - 4}{x - 2})

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Frequently Asked Questions (FAQ)

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)}