Derivative help

102
0
1. The problem statement, all variables and given/known data
(1/2)t^2[(2[tex]\sqrt{t}[/tex])-(1/[tex]\sqrt{t}[/tex])]

2. Relevant equations



3. The attempt at a solution

No matter what I do I get the wrong answer
Things I have tried:
-Expanding the problem, then with the derivatives use the product rule (f)(g') + (g)(f')
 

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
5,453
21
Let's see what you did. Then we can point out where you're going wrong.
 
102
0
=(1/2)t^2[(2t^(1/2)) - (t^(-1/2))]
=t^(5/2) - (1/2)^(3/2)
Use product rule

= ((5/2)t^(3/2))*((-1/2t)^(3/2)) + ((-3/4t)^(1/2))*(t^(5/2))
=(-5/4)t^3 + (-3/4)t^3
= -7/4t^3

Evidently wrong.

The correct answer on the sheet is [([tex]\sqrt{t}[/tex](10t-3)/(4)]
 

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
5,453
21
=(1/2)t^2[(2t^(1/2)) - (t^(-1/2))]
=t^(5/2) - (1/2)^(3/2)
That should be [itex]t^{5/2}-\frac{1}{2}t^{3/2}[/itex] (you're missing the [itex]t[/itex] in the second term).

Use product rule
Why? You don't have a product anymore! Just differentiate term by term.
 
102
0
That should be [itex]t^{5/2}-\frac{1}{2}t^{3/2}[/itex] (you're missing the [itex]t[/itex] in the second term).



Why? You don't have a product anymore! Just differentiate term by term.
What do i do then? ;s

I'm stuck with t^(5/2) - (1/2)t^(3/2)
 

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
5,453
21
What do i do then? ;s
Just differentiate term by term.

Surely you know how to differentiate [itex]at^n[/itex] with respect to [itex]t[/itex], right? :confused:
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top