Question

How do you differentiate `(sqrt(1+3x^2))lnx^2`?

Answer 1

Write it as:
`y=(1+3x^2)^(1/2)ln(x^2)`
and use the Product and Chain Rule:
`y'=1/2(1+3x^2)^(1/2-1)*(6x)ln(x^2)+(1+3x^2)^(1/2)1/x^2*2x=`
`=3xlnx^2/(sqrt(1+3x^2))+2sqrt(1+3x^2)/x=`
`=(3x^2lnx^2+2+6x^2)/(xsqrt(1+3x^2))`