How do you differentiate #f(x) = (sinx)/(e^(x-2)+x)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Sonnhard Jun 2, 2018 #f'(x)=(e^(x-2)*cos(x)+xcos(x)-sin(x)e^(x-2)-sin(x))/(e^(x-2)+x)^2# Explanation: We have #f'(x)=(cos(x)(e^(x-2)+x)-sin(x)(e^(x-2)+1))/(e^(x-2)+x)^2# by the quotient rule Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1279 views around the world You can reuse this answer Creative Commons License