The Chain Rule - Simple but Complicated Problem

[zaboda42]

Find the value of (f o g)' at the given value of x.

f(u) = u⁵ + 1
u = g(x) = sqrt(x)
x = 1

Ok so the section is based on the chain rule and came right out of my calculus book. I seem to be doing the problem right, i check my attempt over a few times and cannot seem to find the problem (the answer in the book is different from my answer).

Here's my attempt:

f(g(x)) = (sqrt(x))⁵ + 1
d/dx ((sqrt(x))⁵) + 1 = (5(sqrt(x)))⁴

Ok the problem is with the derivative of the function. When my book does the problem they get 5/2 but don't explain the procedure. Anyone care to explain, please?

 

[jgens]

Well, it would probably help us if you showed all of your steps but looking at your answer, it looks like you're confused about the application of the chain rule. Try again, showing all of your steps and remember:

$$(f \circ g)'(x) = f'(g(x))g'(x)$$

Edit: It might also help to note that $f(x) = x^5 + 1$ and $g(x) = \sqrt{x}$