How do you differentiate #f(x)=(x^3-2x)(e^x-x^2)# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Tom Jul 3, 2016 #y = (x^3-2x)(e^x-x^2)# #ln(y) = ln(x^3-2x) + ln(e^x-x^2)# #(y')/y = (3x^2-2)/(x^3-2x)+(e^x-2x)/(e^x-x^2)# #y'=y((3x^2-2)/(x^3-2x)+(e^x-2x)/(e^x-x^2))# with #y = (x^3-2x)(e^x-x^2)# it give you #y'=(3x^2-2)(e^x-x^2)+(e^x-2x)(x^3-2x)# 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 1445 views around the world You can reuse this answer Creative Commons License