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

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

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

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

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derivative of

\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})

Simplify

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

= \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}}}

x \to 0 lim (\frac{5 x + 6}{x})

x \to 3 + lim (\frac{x ^{2}}{9 - x ^{2}})

\int 1 x (4 - 2 (x - 3)) d x

(- 5, - 1), (- 1, 5)

x \to 3 - lim (\frac{2}{3 - x})

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