remember differential of lox x is 1/x; if we have a function in place of x we follow chain rule. e.g.,

differential of log (sin x ) = (1/ sinx ) d( sinx)/dx = cosx / sin x and so on.

differential of log ( x^3 + 3x^2 - 4 ) = [1/ ( x^3 + 3x^2 - 4 ) ] * d( x^3 + 3x^2 - 4 )/dx = [1/ ( x^3 + 3x^2 - 4 ) ] * ( 3x^2 + 6x ) so on.