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~ :)
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(4-5) = -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^2-64t√t - 5 / 2√t
c) 20t^2+ 32t√t - 5 / 2√t
d) 20t^2+64t√t - 5 / 2√t
e) 10t^2-32t√t - 5 / √t
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.
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