What is the Derivative of xf(x) at x=4 Using the Product Rule?

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The derivative of the function xf(x) at x=4 is calculated using the product rule. Given that f(4)=7 and f′(4)=−2, the derivative is determined as follows: [xf(x)]' = f(x) + x f'(x). Substituting x=4 yields the result: 7 + 4(-2) = 7 - 8 = -1. Therefore, the derivative of xf(x) at x=4 is -1.

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I am having trouble getting started with this question.
Suppose that f(4)=7 and f′(4)=−2. Use the product rule to find the derivative of xf(x) when x=4. Thanks
 
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musad said:
I am having trouble getting started with this question.
Suppose that f(4)=7 and f′(4)=−2. Use the product rule to find the derivative of xf(x) when x=4. Thanks

It says exactly what to do, use the product rule on $\displaystyle \begin{align*} x\,f(x) \end{align*}$, you should get

$\displaystyle \begin{align*} \left[ x\,f(x) \right] ' &= x' \,f(x) + x\,f'(x) \\ &= 1\,f(x) + x\,f'(x) \\ &= f(x) + x\,f'(x) \end{align*}$

so what do you get when x = 4?
 

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