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) , theny'=(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)
