How do you differentiate #y= (8/x^3)((x + x^7)/5)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Shwetank Mauria Jun 22, 2016 #(dy)/(dx)=-16/(5x^3)+32/5x^3# Explanation: The function #y=(8/x^3)((x+x^7)/5)# = #8/5xx((x+x^7)/x^3)# = #8/5xx(x/x^3+x^7/x^3)# = #8/5xx(1/x^2+x^4)# Hence #(dy)/(dx)=8/5xx((-2)/x^3+4x^3)# or #(dy)/(dx)=-16/(5x^3)+32/5x^3# 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 1467 views around the world You can reuse this answer Creative Commons License