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\frac{d}{dx}\left(\left(\frac{1-2x^3}{1+2x^3}\right)^5\right)

Derive the function ((1-2x^3)/(1+2x^3))^5 with respect to x

Answer

$\frac{5\left(1-2x^3\right)^{4}\left(\frac{-2\left(2x^3+1\right)\frac{d}{dx}\left(x^3\right)-2\left(1-2x^3\right)\frac{d}{dx}\left(x^3\right)}{\left(2x^3+1\right)^2}\right)}{\left(2x^3+1\right)^{4}}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\left(\frac{1-2x^3}{1+2x^3}\right)^5\right)$
1

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

$5\left(\frac{1-2x^3}{2x^3+1}\right)^{4}\cdot\frac{d}{dx}\left(\frac{1-2x^3}{2x^3+1}\right)$

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Answer

$\frac{5\left(1-2x^3\right)^{4}\left(\frac{-2\left(2x^3+1\right)\frac{d}{dx}\left(x^3\right)-2\left(1-2x^3\right)\frac{d}{dx}\left(x^3\right)}{\left(2x^3+1\right)^2}\right)}{\left(2x^3+1\right)^{4}}$
$\frac{d}{dx}\left(\left(\frac{1-2x^3}{1+2x^3}\right)^5\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 3.89 seconds