What is the derivative of

Question

x/(x+1)?

Answer 1

Given x/(x+1)

Apply differentiation

=d/dx(x/(1+x))

Apply differentiation formula: d/dx(f(x)/g(x)) = (g(x)*d/dx(f(x)) - f(x)*d/dx(g(x)))/(g(x))^2

=((x+1)*d/dx(x) - x*d/dx(1+x))/((1+x))^2

=((1+x)*1 - x*(0+1))/(1+x)^2

=(1+x - x(1))/(1+x)^2

=(1+x-x)/(1+x)^2

=1/(1+x)^2

Therefore the derivative of x/(1+x) is 1/(x+1)^2