Final answer to the problem
$\frac{4\left(2\left(3x+2\right)+3\left(-2x+4\right)\right)}{\sqrt{1+\frac{-4x^2+16x-16}{\left(3x+2\right)^2}}\left(3x+2\right)^2}$
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Step-by-step Solution
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1
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
$\frac{d}{dx}\left(4\right)\arcsin\left(\frac{2x-4}{3x+2}\right)+4\frac{d}{dx}\left(\arcsin\left(\frac{2x-4}{3x+2}\right)\right)$
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$\frac{d}{dx}\left(4\right)\arcsin\left(\frac{2x-4}{3x+2}\right)+4\frac{d}{dx}\left(\arcsin\left(\frac{2x-4}{3x+2}\right)\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(4arcsin((2x-4)/(3x+2))). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the constant function (4) is equal to zero. Any expression multiplied by 0 is equal to 0. x+0=x, where x is any expression.
Final answer to the problem
$\frac{4\left(2\left(3x+2\right)+3\left(-2x+4\right)\right)}{\sqrt{1+\frac{-4x^2+16x-16}{\left(3x+2\right)^2}}\left(3x+2\right)^2}$