# How do you find the derivative of # y=sqrt(x−3)# using the limit definition?

##### 1 Answer

Given:

Then:

Using the limit definition:

Substitute in the functions:

We know that, if we multiply the numerator by

Please observe that we have not changed the value of anything, because we have multiplied by 1 in a very special form.

Now, the radicals in the numerator disappear, because of the property

Combine like terms in the numerator:

The h in the numerator cancels with the h in the denominator:

Now we can allow h to become 0:

Combine like terms: