• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Simple Derivitive

  • Thread starter cscott
  • Start date
784
1
How do I deal with the square root in [itex]y = \sqrt{x}(x - 1)[/itex]?
 
788
0
[tex]\sqrt{x} = x^{(\frac{1}{2})}[/tex]

Distribute and take it away.

Also, remember that [tex]a^x*a^y=a^{(x+y)}[/tex]
 
You know the simple formula for deriving powers of x, right? Well, [itex] \sqrt{x}=x^{\frac{1}{2}}[/itex]

EDIT: I was slow. Sorry, I didn't mean chain, I meant distrubution for derivation (didn't know what you call it in English).
 
Last edited:
784
1
Can I get any further that here?

[tex]\left(x - 1\right)\left(\frac{1}{2\sqrt{x}}\right) + \sqrt{x}[/tex]
 
Last edited:
788
0
You're making it more complicated than neccessary.

Distribute the [itex]\sqrt{x}[/itex] then take the derivative.

Ok, your way works, but I wouldn't do it that way. That's the beauty of it though, many correct ways to get the same answer.
 
Last edited:
784
1
[tex]1\frac{1}{2}x^{\frac{1}{2}} - \frac{1}{2}x^{-\frac{1}{2}}[/tex]

correct?
 
788
0
First part is incorrect, second part is correct.
 
784
1
Hmm I don't see how :frown:

[itex]x^{\frac{1}{2}} \cdot x^1 = x^{1.5}[/itex] so doesn't that become [itex]1.5 \cdot x^{\frac{1}{2}}[/itex]?
 
788
0
Oh, ok. You were righting a mixed fraction. It would be best to write 1.5 as [itex]\frac{3}{2}[/itex]

Try not to use mixed fractions, they get too confusing. Use improper ones.

For example: take the derivative of [tex]3\frac{1}{2}\frac{5}{7}x^4[/tex] with respect to x. Make sense?
 
Last edited:
784
1
Jameson said:
Oh, ok. You were righting a mixed fraction. It would be best to call 1.5 [tex]\frac{3}{2}[/tex]

Try not to use mixed fractions, they get too confusion. Use improper ones.
Thanks for the tip and your help (Berislav too) :smile:
 

Physics Forums Values

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