derivative calculus
posted by Steff on .
Please help.
f(t)=(4+√t)(4t^25)
This is what I have so far...
(4+√t)(8t)+(4t^25) (1/2t^1/2)
Am struggling to get this in factored form. Am working on a multiple choice take home test and nothing I am getting matches.

the derivative you got is correct.
by distributing, we can further simplify this into:
32t + 8t^(3/2) + 2t^(3/2)  (5/2)t^(1/2)
10t^(3/2) + 32t  (5/2)t^(1/2)
hope this helps~ :) 
sofar ok
why don't we expand this ... and simplify to get
32t + 10t^(3/2)  (5/2)t^(1/2)
= 32t + 10t√t  5/(2√t)
Since I don't know what your choices are, I don't know in which direction to go from here.
Here is a good trick to see if your answer is the same as theirs.
Pick any point on the original
e.g. let t = 1
f(1) = 5(45) = 5
so (1,5)
so sub in t = 1 into our derivative answer to get
32(1) + 10(1)(1)  5/(2(1)) = 39.5
Any of the choices not giving you 39.5 would be incorrect. 
Here are my options
a) 10t^2+32t√t  5 / √t
b) 20t^264t√t  5 / 2√t
c) 20t^2+ 32t√t  5 / 2√t
d) 20t^2+64t√t  5 / 2√t
e) 10t^232t√t  5 / √t 
added

If c) is written as
(20t^2 + 32t√t  5)/(2√t) it would be same as my answer.
The formed a common denominator
the way you typed it, only the 5 would be divided by 2√t 
Thanks. I see my mistake now.