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