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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{1 - 2 x}{1 + 2 x}) = - \frac{4}{( 1 + 2 x ) ^{2}}

= \frac{1}{2 \frac{1 - 2 x}{1 + 2 x}} (- \frac{4}{( 1 + 2 x ) ^{2}})

Simplify

\frac{1}{2 \frac{1 - 2 x}{1 + 2 x}} (- \frac{4}{( 1 + 2 x ) ^{2}}) : - \frac{2}{- 2 x + 1 ( 2 x + 1 ) ^{\frac{3}{2}}}

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

\frac{d}{d x} (x^{2} sin (x) - x cos (x))

(3 x^{3} + 2 x) (x - 2) (x + 4)

cos (x) d x - sin (y) d y = 0

\int arcsin (d) x d x

n \to \infty lim (1 - n)

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