Question

Find the derivative of f'(x) of f(x)=4sqrt(x) using limits

Answer 1

just use the difference quotient, and recall how to "rationalize" expressions involving roots:

√x - a = (√x-a)(√x+a)/(√x+a)

Answer 2

I did use the difference quotient but got a really weird answer. This was on a test I took earlier this morning and I know we get test corrections once the professor passes the test back

Answer 3

√(x+h)-√x
------------
h

(√(x+h)-√x)(√(x+h)+√x)
--------------------------
h(√(x+h)+√x)

(x+h)-x
-------------------
h(√(x+h)+√x)

h
---------------------
h(√(x+h)+√x)

The h's cancel, and you have

1/(√(x+h)+√x)

As h->0, that is 1/(√x+√x) = 1 / 2√x