Question

@Calculus1 Find the Third Derivative of the function:

F(x)=x^2/X^2-1 @Calculus1 Find the Third Derivative of the function:

F(x)=x^2/X^2-1 @MIT 18.02 Multiva…

Answer 1

what is the denomanator. It is confusing maybe put brackets so i can understand it better

Answer 2

same feeling i do carry as rld x and X what is it

Answer 3

\[2(x-1)/(x^2-1)^2\]

Answer 4

thats just y''

Answer 5

\[f(x)=x^2/x^2-1\] sorry, the capital "X" was a typo. Thank you for the help.

Answer 6

Wait, is it really"
\[f(x)=\frac{x^2}{x^2}-1\]
or do you mean it is:
\[f(x)=\frac{x^2}{x^2-1}\]

Answer 7

The second of the two.

Answer 8

okay.
\[f'(x)= -\frac{2x}{(x^2-1)^2}\]
\[f''(x)= \frac{6x^2+2}{(x^2-1)^3}\]
\[f'''(x)= -\frac{24x(x^2+1)}{(x^2-1)^4}\]

f'(x) can be done with a quotient rule
f''(x) can be done by product rule and then chain rule
f'''(x) product then chain

Answer 9

areene you are wrong at f'(x) step

Answer 10

I got: \[f'(x) = -2x/(2x)^2 \] However, I do not trust my answer.

Answer 11

i m sorry agree was right

Answer 12

For evaluating f'(x)
remember quotient rule:
\[\large\frac{d}{dx}\frac{u}{v}=\frac{v\frac{du}{dx}u\frac{dv}{dx}}{v^2}\]
take u=x^2 and v = x^2-1 and we arrive at:
\[\frac{(x^2-1)(2x)-x^2(\frac{d}{dx}(x^2)-\frac{d}{dx}(1))}{(x^2-1)^2}\]
then we move to:
\[\frac{(x^2-1)(2x)-x^2(2x)}{(x^2-1)^2}\]
combine likes:
\[\frac{-2x}{(x^2-1)^2}\]