How do you differentiate f(x)= x/(x+1) f(x)=xx+1?

2 Answers
Mar 23, 2015

You can use the Quotient Rule where you have:
f(x)=g(x)/(h(x))f(x)=g(x)h(x)
f'(x)=[g'(x)h(x)-g(x)h'(x)]/[h(x)]^2
in your case you get:
f'(x)=[1(x+1)-x*1]/(x+1)^2=1/(x+1)^2

Mar 23, 2015

Use the quotient rule:

(T/B)'=(T'B-TB')/B^2

In this problemf(x)=x/(x+1)

T=x, so T'=1

B=x+1, so B'=1

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