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

How to differentiate (1/y^2 - 3/y^4)(y + 5y^3) for y

  • Thread starter jimen113
  • Start date
  • #1
67
0
1. Homework Statement [/b]

F(y)= (1/y[tex]^{}2[/tex] - 3/y[tex]^{}4[/tex])(y+5y[tex]^{}3[/tex])


Homework Equations


the answer is: F[tex]\acute{}(y)[/tex]=5+14/y[tex]^{}2[/tex]+9/y[tex]^{}4[/tex]

The Attempt at a Solution



In order to use the product formula I brougth the first parenthesis to a common denominator y[tex]^{}4[/tex] and then tried to use the product formula to find the derivative (it didnt work), then I tried subracting 1/y[tex]^{}2[/tex] from 3/y[tex]^{}4[/tex]and then tried to use the product rule. I can't figure out how to use the product/quotient formula to find the derivative, although I have the answer I want to know how to work the problem out.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
249
F(y)= (1/y[tex]^{}2[/tex] - 3/y[tex]^{}4[/tex])(y+5y[tex]^{}3[/tex])
the answer is: F[tex]\acute{}(y)[/tex]=5+14/y[tex]^{}2[/tex]+9/y[tex]^{}4[/tex]
(Yes, that seems to be the right answer.)

Hi jimen! :smile:

No way would I ever use the product rule for this … it's much simpler just to multiply it out, and then differentiate!

But if you want to do it with the product rule as an exercise, that's fine …

I expect you just got a minus in the wrong place - it's easy to do that with inverse powers. :frown:

Can you show us your working (the line f´g + fg´, before expanding), so that we can see what might have gone wrong? :smile:
 
  • #3
67
0
thanks, more questions

Thanks for your immediate reply.
I'm new to the site, so I'm not familiar with typing the math problems:redface:. Basically, I'm having problems typing in the 1st parenthesis in fraction format. At any rate, I found the derivitative of the 1st parenthesis (did it using the power rule)= (-2y[tex]^{}-3[/tex]+12y[tex]^{}-5[/tex]. Then I found the derivative for 2 parenthesis, which is (1+5y[tex]^{}2[/tex]), Now Im stuck, don't know if I should add derivatives together or to multiply them. Suggestions?:confused:
 
  • #4
67
0
where did I go wrong?

RE: F(y)= (1/y - 3/y)(y+5y)
the answer is: F=5+14/y+9/y

F(y)= (f*g)[tex]\acute{}[/tex]
f[tex]\acute{}[/tex]*g)+(f*g[tex]\acute{}[/tex])

(-2y[tex]\hat{}-3[/tex]+12y[tex]\hat{}-5[/tex])*(y+5y[tex]\hat{}3[/tex])+(y[tex]\hat{}-3[/tex]-3y[tex]\hat{}-4[/tex])*(1+15y[tex]\hat{}2[/tex])
so, I get (14/y[tex]\hat{}2[/tex] +9/y[tex]\hat{}4[/tex])+5y,
which is very close to the answer in the book, except that instead of 5y they have the answer as just (14/y[tex]\hat{}2[/tex] +9/y[tex]\hat{}4[/tex])+5
??
 
  • #5
1,631
4
Why do you post twice the same problem????
 
  • #6
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi jimen! :smile:
Basically, I'm having problems typing in the 1st parenthesis in fraction format.
I suggest you "bookmark" http://www.physics.udel.edu/~dubois/lshort2e/node61.html#SECTION008100000000000000000 [Broken]
and http://www.physics.udel.edu/~dubois/lshort2e/node54.html#SECTION00830000000000000000 [Broken]
for all the symbols and techniques.
(-2y[tex]\hat{}-3[/tex]+12y[tex]\hat{}-5[/tex])*(y+5y[tex]\hat{}3[/tex])+(y[tex]\hat{}-3[/tex]-3y[tex]\hat{}-4[/tex])*(1+15y[tex]\hat{}2[/tex])
Yes - I thought so - you've just put [tex]y^{-3}[/tex] in the second part instead of [tex]y^{-2}[/tex]

Try it again! :smile:
[size=-2](if you're happy, don't forget to mark thread "solved"!)[/size]​
 
Last edited by a moderator:
  • #7
118
0
Hi jimen! :smile:

I suggest you "bookmark" http://www.physics.udel.edu/~dubois/lshort2e/node61.html#SECTION008100000000000000000 [Broken]
and http://www.physics.udel.edu/~dubois/lshort2e/node54.html#SECTION00830000000000000000 [Broken]
for all the symbols and techniques.
either that or just use mathtype and its translation tool ;)
 
Last edited by a moderator:
  • #8
tiny-tim
Science Advisor
Homework Helper
25,832
249
either that or just use mathtype and its translation tool ;)
ooh! what's mathtype? :smile:
 
  • #9
67
0
either that or just use mathtype and its translation tool ;)
Thanks!
 
  • #10
67
0
Thanks for your help, it worked!
 

Related Threads for: How to differentiate (1/y^2 - 3/y^4)(y + 5y^3) for y

Replies
12
Views
1K
Replies
7
Views
1K
Replies
2
Views
737
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
16
Views
1K
Top