Differentiate e^fx: Solving 2xe^(2x)

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SUMMARY

The discussion focuses on differentiating the function f(x) = xe^(2x) using the product rule. The user correctly applies the product rule, resulting in the expression xe^(2x) + e^(2x). However, the final answer provided, 2xe^(2x), is incorrect as it neglects the derivative of e^(2x) which requires the application of the chain rule. The correct derivative is f'(x) = e^(2x) + 2xe^(2x).

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CrossFit415
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f(x)= xe^(2x)

So I applied the product rule
(f • g) = x • e(^2x) + e^(2x) • 1
= xe^(2x) + e^(2x)
=2xe^(2x)

And got this as my final answer.

Would I need to use chain rule? Did I do this correctly?
 
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CrossFit415 said:
f(x)= xe^(2x)


(f • g)' = x • e(^2x) + e^(2x) • 1
You forgot to take the derivative of e^(2x)
 

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