How do you differentiate #f(x)=ln2x * cos3x# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Konstantinos Michailidis Feb 21, 2016 It is #(df(x))/dx=(d(ln2x))/dx*cos3x+ln2x*(d(cos3x))/dx=> (df(x))/dx=[((2x)')/(2x)]*cos3x+ln2x*(-sin3x)*3=> (df(x))/dx=(cos3x)/x-3ln2x*sin3x# 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 1793 views around the world You can reuse this answer Creative Commons License