Question

How do you differentiate `f(x)= 2xlnx` using the product rule?

Answer 1

`d/dx2xln(x) =2(ln(x) + 1)`

Explanation:

The product rule states
`d/dxf(x)g(x) = f'(x)g(x) +f(x)g'(x)`

In this case, we have `f(x) =2x` and `g(x) = ln(x)`
`d/dx2x = 2`
`d/dx ln(x) = 1/x`

So

`d/dx2xln(x) = 2*ln(x) + 2x*1/x = 2(ln(x) + 1)`