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Step-by-step Solution

Find the derivative of $\frac{-1}{\sqrt{\frac{1-x}{1+x}}\left(1+x\right)^2}$

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Answer

$\frac{\frac{3}{2}\sqrt{1+x}\left(1-x\right)-\frac{1}{2}\sqrt{\left(1+x\right)^{3}}}{\sqrt{\left(1-x\right)^{3}}\left(1+x\right)^{3}}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\frac{-1}{\sqrt{\frac{1-x}{1+x}}\left(1+x\right)^2}\right)$
1

The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\frac{d}{dx}\left(\frac{-1}{\left(1+x\right)^2\frac{\sqrt{1-x}}{\sqrt{1+x}}}\right)$
2

Multiplying the fraction and term

$\frac{d}{dx}\left(\frac{-1}{\frac{\sqrt{1-x}\left(1+x\right)^2}{\sqrt{1+x}}}\right)$

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Answer

$\frac{\frac{3}{2}\sqrt{1+x}\left(1-x\right)-\frac{1}{2}\sqrt{\left(1+x\right)^{3}}}{\sqrt{\left(1-x\right)^{3}}\left(1+x\right)^{3}}$
$\frac{d}{dx}\left(\frac{-1}{\sqrt{\frac{1-x}{1+x}}\left(1+x\right)^2}\right)$

Main topic:

Differential calculus

Related formulas:

6. See formulas

Time to solve it:

~ 0.21 seconds