`y= ln x^(cos12x) `

`==gt y= (cos12x)(lnx)`

Now we will use the product rule to find the derivative.

`==gt y' = (cos12x)'(lnx) + (cos12x)(lnx)' `

`==gt y'= (-12sinx)(lnx) + (cos12x)(1/x) `

`==gt y'= -12(sinx)lnx + (cos12x)/x`

`y= ln x^(cos12x) `

`==gt y= (cos12x)(lnx)`

Now we will use the product rule to find the derivative.

`==gt y' = (cos12x)'(lnx) + (cos12x)(lnx)' `

`==gt y'= (-12sinx)(lnx) + (cos12x)(1/x) `

`==gt y'= -12(sinx)lnx + (cos12x)/x`