How do I find the derivative of the function #f(x) = 9x^2 ln(8x)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Sonnhard Jun 2, 2018 #f'(x)=18xln(8x)+9x# Explanation: By the product and chain rule we get #f'(x)=18xln(8x)+9x^2*1(8x)*8# #f'(x)=18xln(8x)+9x=9x(2ln(8x)+1)# 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 5544 views around the world You can reuse this answer Creative Commons License