Question

How do you differentiate `g(x) = xe^(2x)lnx` using the product rule?

Answer 1

The product rule for three functions `f,g,h` is as follows

`(f*g*h)'=(df)/dx*g*h+f*(dg)/dx*h+f*g*(dh)/dx`

Hence apply the above rule you get

`d/dx(x e^(2 x) ln(x)) = e^(2 x) (2 x ln(x)+ln(x)+1)`