How do you find the derivative of #(3x-2)^10 * (5x^2-x+1)^12#? Calculus Basic Differentiation Rules Product Rule 1 Answer Massimiliano May 14, 2015 In this way: #y'=[10(3x-2)^9*3] * (5x^2-x+1)^12+# #+(3x-2)^10*[12(5x^2-x+1)^11*(10x-1)]=# #=6(3x-2)^9(5x^2-x+1)^11 * [5(5x^2-x+1)+2(3x-2)(10x-1)]=# #=6(3x-2)^9(5x^2-x+1)^11 * (25x^2-5x+5+60x^2-6x-40x+4)=# #=6(3x-2)^9(5x^2-x+1)^11(85x^2-51x+9)=#. 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 7441 views around the world You can reuse this answer Creative Commons License