How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ?
1 Answer
Jul 30, 2014
#y'=1/(3+e^x)-xe^x/((3+e^x)^2)# Explanation,
Using Quotient Rule,
#y=f(x)/g(x)# , then#y'=(f'(x)g(x)−f(x)g'(x))/(g(x))^2# Similarly following for
#y=x/(3+e^x)# differentiating both side with respect to
#x# ,
#dy/dx=d/dx(x/(3+e^x))#
#y'=((3+e^x)(x)'-x(3+e^x)')/((3+e^x)^2#
#y'=((3+e^x)-x(e^x))/((3+e^x)^2#
#y'=((3+e^x)-x(e^x))/((3+e^x)^2#
#y'=1/(3+e^x)-xe^x/((3+e^x)^2)#
