How do you differentiate #(sqrt(1+3x^2))lnx^2#? Calculus Basic Differentiation Rules Product Rule 1 Answer GiĆ³ May 1, 2015 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))# Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x - 3)(2 - 3x)(5 - x)# ? How do you use the product rule to find the derivative of #y=x^2*sin(x)# ? How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? How do you apply the product rule repeatedly to find the derivative of #f(x) = (x^4 +x)*e^x*tan(x)# ? How do you use the product rule to find the derivative of #y=(x^3+2x)*e^x# ? How do you use the product rule to find the derivative of #y=sqrt(x)*cos(x)# ? How do you use the product rule to find the derivative of #y=(1/x^2-3/x^4)*(x+5x^3)# ? How do you use the product rule to find the derivative of #y=sqrt(x)*e^x# ? How do you use the product rule to find the derivative of #y=x*ln(x)# ? See all questions in Product Rule Impact of this question 1339 views around the world You can reuse this answer Creative Commons License