How do you differentiate #f(x)=csc5x * cot3x# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Monzur R. Jun 27, 2017 #f'(x) = -3csc5xcsc^2 3x -5csc5xcot5xcot3x# Explanation: Product rule: #(uv)' = vu' +uv'# Let #u=cot3xrArr u' = -3csc^2 3x# And #v=csc5x rArr v'= -5csc5xcot5x# Then #(csc5x*cot3x)' = -3csc^2 3xcsc5x - 5csc5xcot5xcot3x# 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 1113 views around the world You can reuse this answer Creative Commons License