How do you find the derivative of #Y= ( 5x + 3 )( x - 7)^(-1/3)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Massimiliano Jun 3, 2015 In this way with the product rule: #y'=5(x-7)^(-1/3)+(5x+3)(-1/3)(x-7)^(-1/3-1)=# #=1/3(x-7)^(-4/3)*[3*5*(x-7)^(-1/3-(-4/3))-(5x+3)*1]=# #=1/3(x-7)^(-4/3) * [15*(x-7)-5x-3]=# #=1/3(x-7)^(-4/3)(10x+102)=# #=2/3(x-7)^(-4/3)(5x+51)#. 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 1483 views around the world You can reuse this answer Creative Commons License