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

Derive the function ((1-2x)/(1+x))^3 with respect to x

Answer

$\frac{12x^2\frac{-2\left(x+1\right)-\left(1-2x\right)}{\left(x+1\right)^2}-12x\frac{-2\left(x+1\right)-\left(1-2x\right)}{\left(x+1\right)^2}+3\frac{-2\left(x+1\right)-\left(1-2x\right)}{\left(x+1\right)^2}}{\left(x+1\right)^{2}}$

Step-by-step explanation

Problem

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

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

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

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Answer

$\frac{12x^2\frac{-2\left(x+1\right)-\left(1-2x\right)}{\left(x+1\right)^2}-12x\frac{-2\left(x+1\right)-\left(1-2x\right)}{\left(x+1\right)^2}+3\frac{-2\left(x+1\right)-\left(1-2x\right)}{\left(x+1\right)^2}}{\left(x+1\right)^{2}}$
$\frac{d}{dx}\left(\left(\frac{1-2x}{1+x}\right)^3\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.52 seconds