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** Step-by-step Solution **

Problem to solve:

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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\sqrt{2x+6}$

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$\frac{d}{dx}\left(x\right)\sqrt{2x+6}+x\frac{d}{dx}\left(\sqrt{2x+6}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of x(2x+6)^1/2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{2x+6}. The derivative of the linear function is equal to 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}. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

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