Expert: Paul Klarreich - 10/7/2009

Question
Can you help me work through this expression?  Thanks
Suppose that
f (x) = sqrt (5x+1)/(4x^2+1)  (the entire equation is in the square root)

Find f'(x), and then evaluate f ' at x = 2.
f'(2)=__________________________

Answer
Questioner: mikel
Country: United States
Category: Calculus
Private: No
Subject: calculus-differentiation rules
Question: Can you help me work through this expression?  Thanks
Suppose that
f (x) = sqrt (5x+1)/(4x^2+1)  (the entire eXPRESSION is in the square root)

Find f'(x), and then evaluate f ' at x = 2.
f'(2)=__________________________

........................................................

If

f(x) = sqrt[ (5x+1)/(4x^2+1)]  << that is how to write it.

Write:

f(x) = [ (5x+1)/(4x^2+1) ]^1/2

Use the chain rule:

f(u) = u^1/2,   and  u = (5x+1)/(4x^2+1)
          1
f'(u) = --------
       2 u^1/2

and use the quotient rule to get  u'(x):
    (4x^2+1)(5) - (5x+1)(8x)
u' = -------------------------
            (4x^2 + 1)^2

Simplify that, then put it all together.