Answer:
[tex]y' =2^x ( 1 + xln 2 )[/tex]
Step-by-step explanation:
given,
[tex]y= x\ 2^x[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{\mathrm{d} }{\mathrm{d} x}(x\ 2^x )[/tex]
using chain rule
[tex]y'= x (2^x ln 2) + 2^x(1)[/tex]
[tex]y' = 2^x + x (2^x ln 2)[/tex]
[tex]y' =2^x ( 1 + xln 2 )[/tex]
hence the answer is given above.
