Use the product rule to find the derivative of the following. $y=(x+5)(3\sqrt{x}+5)$ What is the result of applying the product rule on y? OA. $y'=\frac{d}{dx}(x+5) \cdot \frac{d}{dx}(3\sqrt{x}+5)$ OB. $y'=(x+5) \cdot \frac{d}{dx}(3\sqrt{x}+5) + (3\sqrt{x}+5) \cdot \frac{d}{dx}(x+5)$ OC. $y'=\frac{d}{dx}(x+5) + \frac{d}{dx}(3\sqrt{x}+5)$ OD. $y'=\frac{d}{dx}(x+5) \cdot \frac{d}{dx}(3\sqrt{x}+5) + (x+5) \cdot (3\sqrt{x}+5)$ Find the derivative. $y'=$ (Use integers or fractions for any numbers in the expression.)
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In this case, $u(x) = (x+5)$ and $v(x) = (3\sqrt{x}+5)$. So, $y' = \frac{d}{dx}(x+5) \cdot (3\sqrt{x}+5) + (x+5) \cdot \frac{d}{dx}(3\sqrt{x}+5)$. This corresponds to option B. Show more…
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