How do you use the product Rule to find the derivative of #h(t)=t^(1/3)(t^2+4)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Nallasivam V Aug 18, 2015 #dy/dt# = [#t^(1/3)# (2t)] +[ (#t^2# + 4) (#1/3##t^(-2/3)#)] #dy/dt#=[#2t^(4/3)# ] +[ (#t^2# + 4) (#1/(3t^(2/3)#)] #dy/dt#=[#2t^(4/3)# ] +[ # (t^2 + 4)/(3t^(2/3)#] #dy/dt#= # (6t^2+t^2 + 4)/(3t^(2/3)# #dy/dt#= # (7t^2 + 4)/(3t^(2/3)# 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 1361 views around the world You can reuse this answer Creative Commons License