How do you use the product rule to differentiate #y=cos(x)*sin(x)# ? Calculus Basic Differentiation Rules Product Rule 1 Answer AJ Speller Oct 20, 2014 #y=u*v=cos(x)*sin(x)# #u'=-sin(x)# #v'=cos(x)# #y'=(uv)'=u'v+uv'=-sin(x)*sin(x)+cos(x)*cos(x)# #y'=(uv)'=u'v+uv'=-sin^2(x)+cos^2(x)# 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 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)# ? What is the derivative of #xe^x#? See all questions in Product Rule Impact of this question 6979 views around the world You can reuse this answer Creative Commons License