Question

How do you differentiate `[(e^x)(lnx)]/x`?

Answer 1

`e^x/x^2(1+(x-1)lnx)`

Explanation:

`f(x) = (e^xlnx)/x`

`f'(x) = (x(e^x*1/x+e^xlnx)-e^xlnx*1)/x^2`
(Quotient rule and Produce rule)

`f'(x) = (e^x+xe^xlnx-e^xlnx)/x^2`

`= e^x/x^2(1+(x-1)lnx)`