How do you differentiate #f(x)=sinxcosx# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Roella W. Jan 8, 2016 #f'(x)=cos^2x - sin^2x# or # 1-2sin^2x# Explanation: The product rule states that if #f(x) = g(x)h(x)# then # f'(x) = g(x)h'(x) + g'(x)h(x)# #f(x) = sinxcosx# #:.f'(x) = sinx(-sinx) +cosxcosx# 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 2093 views around the world You can reuse this answer Creative Commons License