How do you differentiate #f(x)= (4x^2-1) *ln x# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer James May 28, 2018 #y'=(4x^2-1)*1/x+lnx*8x# Explanation: The product Rule: #color(red)[y=f(x)*g(x)]# #color(red)[y'=f(x)*g'(x)+g(x)*f'(x)]# now lets derive #color(blue)[y= (4x^2-1) *ln x]# #y'=(4x^2-1)*1/x+lnx*8x# 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 1786 views around the world You can reuse this answer Creative Commons License