How do you differentiate #g(x) =e^(1-x)tanx# using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Bdub Apr 8, 2016 #g'(x)=e^(1-x)sec^2x -e^(1-x)tanx# Explanation: let #f=e^(1-x)# and #g=tanx# #f'=e^(1-x)*-1, g'=sec^2x# #g'(x) = fg'+gf'# #g'(x)=e^(1-x)sec^2x -e^(1-x)tanx# 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 1181 views around the world You can reuse this answer Creative Commons License