How do you use the Product Rule to find the derivative of #f(x)=cot(x)cos(x)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Dharma R. Sep 22, 2015 #-cosx-cotxcosecx# Explanation: let #u(x)= cotx ##v(x)=cosx##,f(x)=u(x)v(x)# according to product rule# d(uv)/dx=udv/dx+vdu/dx# #d(cotxcossx)/dx=cotx(dcosx/dx)+cosx(d/dx(cotx)) =cotx(-sinx)+cosx(-cosec^2x)=-cosx-cotxcosecx# 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 1931 views around the world You can reuse this answer Creative Commons License