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.
