i think im doing the mistake there.
is the derivative of y= 4+ ln(x+1) 1/(x+1) or 4/ (x+1) ?
Neither. The derivative of "4" is "0" and the derivative of "ln(x+1)" is "$\displaystyle \frac{1}{x+1}$". The derivative of the sum f+ g is f'+ g' so the derivative of 4+ ln(x+1) is $\displaystyle 0+ \frac{1}{x+1}= \frac{1}{x+1}$.