What is the derivative of #f(x) = x^2(x-2)^4#? Calculus Basic Differentiation Rules Product Rule 1 Answer Shwetank Mauria Apr 6, 2016 #(df)/(dx)=2x(x-2)^3(3x-2)# Explanation: Product rule states that if #f(x)=g(x)*h(x)# #(df)/(dx) = g(x)xx(dh)/(dx) + h(x)xx(dg)/(dx) # Here #g(x)=x^2# and #h(x)=(x-2)^4# Hence, #(df)/(dx)=x^2xx4(x-2)^3+(x-2)^4xx2x# = #2x(x-2)^3{2x+(x-2)}# = #2x(x-2)^3(3x-2)# 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 2972 views around the world You can reuse this answer Creative Commons License