3.98: Product rule and related integral

0606/23/M/J/22 — Question 8 · 6 marks

(a)
Differentiate y=2xe4xy = 2x\mathrm{e}^{4x} with respect to xx.
[2]
(b)
Hence find xe4xdx\displaystyle\int x\mathrm{e}^{4x}\,\mathrm{d}x.
[4]