Question

Find the first and second derivative of h(x) = sqrt of (x^2-1)

Answer 1

\[h(x) = \sqrt{x ^{2}+1}\]

Answer 2

h'=1/2(x^2+1)^-1/2 (2x)\[x \over \sqrt{x ^{2}+1}\]Gotta watch Hawaii 50 now will get back later.

Answer 3

y did u multiply it by 2x at teh end?

Answer 4

Never mind it is an hour from now.
Now we have x(x^2+1.......oops I should be working with (x^2 -1)^-1/2 which is it\[\sqrt{x ^{2}-1}\] or\[\sqrt{x ^{2}+1}\]

Answer 5

teh second one

Answer 6

Good used the chain rule.

Answer 7

so teh first der of teh function is x/sqrt of (x^2+1)

Answer 8

Yes, let me copy the chain rule, or are you already familiar with it?

Answer 9

i heard of it thou its jsut confusing..if u can expalin it taht wud b great

Answer 10

wait was is teh second der?

Answer 11

I'm with you, I will show you an example:
d/dx of the following:\[(x ^{2}-5x+1)^{10}=10(x ^{2}-5x+1)^{9}(2x-5)\]
did you get the idea?

Answer 12

yes i get the idea

Answer 13

Now for the second derivative I will express the first derivative in this manner:\[x(x ^{2}+1)^{-1/2}\] do you agree that we can now use the product rule?

Answer 14

yes

Answer 15

so after teh product rule what does it become

Answer 16

Let me do it: and maybe we will see.

\[1\times(x ^{2}+1)^{-1/2}+x \times-1/2(x ^{2}+1)^{-3/2}\times2x\]That is it now to simplify it to the final product. I will put it in the next frame.

Answer 17

can u expalin wat u just did now

Answer 18

Used the product rule The product rule states:\[d/dx \left[ f .g\right]=f'.g + f.g'\]The periods should be dots meaning multiply.

Answer 19

In words: derivative of the first, times the second plus first times derivative of the second.

Answer 20

ok i understand taht

Answer 21

so wen simplified what does the answer become

Answer 22

Let me see if i can straighten that bad boy out.lol

Answer 23

lmao

Answer 24

\[1/(x ^{2}+1)^{-1/2}-x ^{2}/(x ^{2}+1)^{-3/2}\]It can be simplified further if you would do the actual subtraction which I will do if I can figure out the LCD.

Answer 25

Let me make a correction, the two exponents -1/2 and -3/2 should be positive when I placed them in the denominator. Hawaii 50 is now on, will be back later.

Answer 26

ok

Answer 27

i can write it for you if you like using quotient rule rather than product rule

Answer 28

I'm back. Let me express it correctly:
\[1/(x ^{2}+1)^{1/2}-x ^{2}/(x ^{2}+1)^{3/2}\]

Answer 29

This would then become:\[(x ^{2}+1)/(x ^{2}+1)^{3/2}-x ^{2}/(x ^{2}+1)^{3/2}\] then combining \[1\over(x ^{2}+1)^{3/2}\] for a final answer. Hopefully satellite73 will review this for confirmation.

Answer 30

@satallite ..that would be good...srry i logged off yesterday by teh time u replied