Question

Find the derivative

y=x(2^x)

y’=

Answer 1

`y' =2^x ( 1 + xln 2 )`

Explanation:

given,

`y= x\ 2^x`

`\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{\mathrm{d} }{\mathrm{d} x}(x\ 2^x )`

using chain rule

`y'= x (2^x ln 2) + 2^x(1)`

`y' = 2^x + x (2^x ln 2)`

`y' =2^x ( 1 + xln 2 )`

hence the answer is given above.