Use the table to find the given derivative. (Hint: You may need to use the Product Rule) d / dx [xf(x)] x=3 x 1 2 3 4 5 f(x) 5 4 3 2 1 f'(x) 1 2 4 5 3
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Step 1
Step 1:** Apply the Product Rule to find the derivative of xf(x) with respect to x: \[ \frac{d}{dx}[xf(x)] = x \cdot f'(x) + f(x) \] ** Show more…
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Use the following table to find the given derivatives. $$\begin{array}{lclclclc} x & 1 & 2 & 3 & 4 \\ \hline f(x) & 5 & 4 & 3 & 2 \\ f^{\prime}(x) & 3 & 5 & 2 & 1 \\ g(x) & 4 & 2 & 5 & 3 \\ g^{\prime}(x) & 2 & 4 & 3 & 1 \end{array}$$ $$\left.\frac{d}{d x}(x f(x))\right|_{x=3}$$
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Use the table to find the following derivatives. $$\begin{array}{cccccc} x & 1 & 2 & 3 & 4 & 5 \\ \hline f^{\prime}(x) & 3 & 5 & 2 & 1 & 4 \\ g^{\prime}(x) & 2 & 4 & 3 & 1 & 5 \end{array}$$ $$\left.\frac{d}{d x}(f(x)+g(x))\right|_{x=1}$$
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Use the following table to find the given derivatives. $$\begin{array}{lclclclc} x & 1 & 2 & 3 & 4 \\ \hline f(x) & 5 & 4 & 3 & 2 \\ f^{\prime}(x) & 3 & 5 & 2 & 1 \\ g(x) & 4 & 2 & 5 & 3 \\ g^{\prime}(x) & 2 & 4 & 3 & 1 \end{array}$$ $$\left.\frac{d}{d x}\left(\frac{f(x) g(x)}{x}\right)\right|_{x=4}$$
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