How do you differentiate # (2x+1)(x-tanx)#? Calculus Basic Differentiation Rules Product Rule 1 Answer Shwetank Mauria Jun 15, 2016 #d/(dx)(2x+1)(x-tanx)# = #4x+1-2xsec^2x-sec^2x-2tanx# Explanation: If #f(x)=g(x)xxh(x)#, #(df)/(dx)=g(x)xx(dh)/(dx)+(dg)/(dx)xxh(x)# Hence #d/(dx)(2x+1)(x-tanx)# = #(2x+1)(1-sec^2x)+2(x-tanx)# = #2x+1-2xsec^2x-sec^2x+2x-2tanx# = #4x+1-2xsec^2x-sec^2x-2tanx# 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 1464 views around the world You can reuse this answer Creative Commons License