How do you differentiate $y = \frac{x}{x + 1}$ $y = (x) / (x+1)$ ?

Question

1745 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-25T13:12:47

We can use the quotient rule, which states that for $y = \frac{f (x)}{g (x)}$ $y=f(x)/g(x)$ , $(dy)/(dx)=(f'(x)g(x)-f(x)g'(x))/g(x)^2$

Following the formula:

$(dy)/(dx)=((1)(x+1)-(x)(1))/(x+1)^2=(x+1-x)/(x+1)^2=1/(x+1)^2=(x+1)^(-2)$

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