Question

How do you differentiate `f(x)=(lnx+x)(1+e^x)` using the product rule?

Answer 1

• Product rule: `(ab)'=a'b+ab'`

Explanation:

`(df(x))/(dx)=(1/x+1)(1+e^x)+(lnx+x)(e^x)`

`(df(x))/(dx)=(e^x/x+e^x+1/x+1)+(e^xlnx+xe^x)`

`(df(x))/(dx)=e^x(1+1/x+lnx+x)+1/x+1`