Question

HIGHER DERIVATIVES

Answer 1

\[x = \frac{ 1 }{ t-1 }\]

Answer 2

\[y=\frac{ t }{ t^2-1 }\]

Answer 3

find 1st, 2nd and 3rd derivatives

Answer 4

\[\frac{ dy }{ dx }\]

Answer 5

\frac{ d^2y }{ dx^2 }

Answer 6

\[\frac{ d^2y }{ dx^2 }\]

Answer 7

\[\frac{ d^y }{ dx^3 }\]

Answer 8

So, you need to find the first second and third derivatives yeah?
Well, you have;

\(x=\dfrac{1}{t-1}\)

Can you find the derivative of this?

Answer 9

yes

Answer 10

it's \[dx/du =\frac{ -1 }{ t^2-1 }\]

Answer 11

\[dy/du = \frac{ -t^2-1 }{ (t^2-1)^2 }\]

Answer 12

\(\dfrac{dx}{dt}=\dfrac{-1}{(t-1)^2}\)

This is what you should have, that is the first order derivative.
Your second order derivative is the derivative of that just above.

Answer 13

oops

Answer 14

sorry I've made a mistake

Answer 15

Now, what is the derivative of the first derivative?
\(\large{x^{\prime}=\dfrac{-1}{(t-1)^2}}\)

Answer 16

\[dy/dx\]

Answer 17

:D

Answer 18

then find \[\frac{ d^2y }{ dx^ }\]

Answer 19

divide dy by dx