Question

How do you differentiate `f(x)=log_3(xe^x)`?

Answer 1

`1/ln3` (`1/x` + 1)

First change the base to natural log, f(x)= ln(x`e^x`) /ln3.

Now differeentiate f' (x) = `1/ln3` `d/dx` ln(x`e^x`)

=`1/ln3` `d/dx` (lnx + x)

= `1/ln3` ( `1/x` +1)