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

We can use the quotient rule, which states that for

Following the formula:

By signing up, you agree to our Terms of Service and Privacy Policy

To differentiate the function ( y = \frac{x}{x+1} ), we can use the quotient rule, which states that for a function ( \frac{u}{v} ), the derivative is given by ( \frac{u'v - uv'}{v^2} ), where ( u' ) represents the derivative of ( u ) with respect to ( x ) and ( v' ) represents the derivative of ( v ) with respect to ( x ). Applying this rule to ( y = \frac{x}{x+1} ), we have:

( u = x ) and ( v = x + 1 )

( u' = 1 ) (derivative of ( x )) and ( v' = 1 ) (derivative of ( x + 1 ))

Plugging these values into the quotient rule formula:

( y' = \frac{(1)(x+1) - (x)(1)}{(x+1)^2} )

( y' = \frac{x+1 - x}{(x+1)^2} )

( y' = \frac{1}{(x+1)^2} )

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7