The following formulas may be use in this problem
#d/dx(u/v)=(v*d/dx(u)-u*d/dx(v))/v^2#
also
#d/dx(ln u)=1/u*d/dx(u)#
From the given #f(x)=3ln(e^(x^2+1)/(2x^3))#
#f' (x)=d/dx(3ln(e^(x^2+1)/(2x^3)))#
#f' (x)=3*d/dx(ln(e^(x^2+1)/(2x^3)))#
#f' (x)=3*(1/(e^(x^2+1)/(2x^3)))*d/dx(e^(x^2+1)/(2x^3))#
#f' (x)=3*((2x^3)/(e^(x^2+1)))*(((2x^3)d/dx(e^(x^2+1))-(e^(x^2+1))d/dx(2x^3))/(2x^3)^2)#
#f' (x)=3*((2x^3)/(e^(x^2+1)))*((2x^3)(e^(x^2+1))d/dx(x^2+1)-(e^(x^2+1))(6x^2))/(2x^3)^2#
#f' (x)=3*((2x^3)/(e^(x^2+1)))*((2x^3)(e^(x^2+1))(2x)-(e^(x^2+1))(6x^2))/(2x^3)^2#
#f' (x)=3*((2x^3)/cancel(e^(x^2+1)))*((4x^4-6x^2)cancel(e^(x^2+1)))/(2x^3)^2#
#f' (x)=3*((2x^4-3x^2))/(x^3)#
#f' (x)=3*((2x^2-3))/(x)#
God bless...I hope the explanation is useful.
