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}}}

x \to 3 lim (6 f (x) + 2 x)

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

(25 + x^{2}) y^{^{'}} - 2 x y = 0

\frac{d y}{d x}, x y = 54

\frac{d}{d x} (x 3 x^{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)}