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

Which rules to use (Product rule?)

  • Thread starter BOAS
  • Start date
  • #1
555
19

Homework Statement



Find the gradient of the curve at the given point on the curve

y = [itex]\frac{(√x - 1)}{√x}[/itex] where x = 9

Homework Equations



y(x) = u(x)v(x)

dy/dx = u(dv/dx) + v(du/dx)

The Attempt at a Solution



my problem really boils down to rearranging the function to a form easy to manipulate so i'll show you how far I get and where I think i'm going wrong.

y = [itex]\frac{(√x - 1)}{√x}[/itex]

y = (x1/2-1)x-1/2

Here, i'm not sure whether the first bracket should read (x1/2-1) or (x-1)1/2.

Treating it as y = (x1/2-1)x-1/2 I can apply the product rule easily enough, but if I were to expand out those brackets I get y =[itex]1 - x^{-1/2}[/itex] which when I put into a graphing program is slightly different to the original...

I'm pretty sure i've treated the brackets in the original equation wrong with respect to the square root.

If you could help clear this up for me, that would be great!
 

Answers and Replies

  • #2
FeDeX_LaTeX
Gold Member
437
13
You need only use the power rule here. Do you see why?
 

Related Threads on Which rules to use (Product rule?)

Replies
21
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
6
Views
1K
Replies
1
Views
1K
Replies
17
Views
7K
  • Last Post
Replies
7
Views
772
Replies
1
Views
845
Replies
2
Views
830
Replies
1
Views
1K
Top