Let $$y(x)= 4 x^3 e^{2x},$$
then
$$y'(x) = 4 \times 3 \, x^2 e^{2x} + 4 \, x^3 \times 2 e^{2x} = 12 \, x^2 e^{2x} + 8 \, x^3 e^{2x}$$
Does this look correct?
2026-03-29 16:24:32.1774801472
Differentiate the following functions
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Yes, you result is correct. If you're uncertain in the future you may also like to use Wolfram|Alpha, see http://www.wolframalpha.com/input/?i=d%2Fdx+4x^3e^%282x%29 for this result. It does also provide a step-by-step solution.