Question

How do you differentiate `y=ln(3xe^(1-x))`?

Answer 1

`(1-x)/x`.

Explanation:

`y=ln(3xe^(1-x))`.

Using the usual rules of log function, we have,

`y=ln3+lnx+lne^(1-x), or,`

`y=ln3+lnx+(1-x)lne=ln3+lnx+1-x`.

`:. dy/dx=0+1/x+0-1`.

`rArr dy/dx=(1-x)/x`, as Respected Sonnhard has derived!