Question

Question #42acc

Answer 1

`y'=1/(x+1)^2`

Explanation:

Apply the quotient rule:

`y'=d/dx(f(x)/g(x))=(d/dx[f(x)]g(x)-d/dx[g(x)]f(x))/(g(x))^2`

Given: `(2x+1)/(x+1)`

Let

`f(x)=2x+1=>d/dx[f(x)]=2`

`g(x)=x+1=>d/dx[g(x)]=1`

Substituting into the quotient rule

`y'=((2)(x+1)-(1)(2x+1))/(x+1)^2`

Simplifying:

`y'=((2x+2)-(2x+1))/(x+1)^2=((cancel(2x)+2)-(cancel(2x)+1))/(x+1)^2=1/(x+1)^2`