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