Question

differentiate (t-1/t)(t^2-1/t^2)

Answer 1

no look more closely

Answer 2

Is it
\((t-\frac{1}{t})(t^2-\frac{1}{t^2})\) in your question?

Answer 3

thats better

Answer 4

If it is the case, I suggest you to expand the factor first.

Answer 5

if i knew how to complete that succesfully i wouldn't have put my question on open study

Answer 6

Can you try expanding the factors first?

Answer 7

You can also use product rule and power rule.
\[(f\cdot g) ^\prime (x) = f^\prime g + f g^\prime\]
\[f = x^n \Rightarrow f^\prime (x) =n \cdot x^{n-1} \]

Answer 8

Hint: \((t-\frac{1}{t})(t^2-\frac{1}{t^2})\) = \(t(t^2-\frac{1}{t^2}) - \frac{1}{t}(t^2-\frac{1}{t^2})\)

Answer 9

yes that i have done but i,m stuck just a little further up than that

Answer 10

The reason why I'm not using product rule is because expanding it seems to be a easier way. But you can use the product rule of course.

Answer 11

and so what next

Answer 12

What have you got by expanding it?

Answer 13

t^3-1/t^3-1/t^2+1/t^2

Answer 14

make the last product 1/t^3

Answer 15

both 1/t^3 cancel and i,m left with t^3-1/t^2

Answer 16

You'd better check your calculation again..

Answer 17

i have several times

Answer 18

\[t(t^2-\frac{1}{t^2}) - \frac{1}{t}(t^2-\frac{1}{t^2})\]\[=t(t^2)-(t)(\frac{1}{t^2}) - \frac{1}{t}(t^2)-(\frac{1}{t})(\frac{1}{t^2})\]\[=...?\]

Answer 19

thats what i got

Answer 20

And can you simplify that?

Answer 21

t^3-1/t^3-1/t^3-2/t^3

Answer 22

how's the calculus coming along?

Answer 23

\[t (\frac{1}{t^2}) = \frac{t}{t^2} = \frac{1}{t}\], not 1/t^3

Answer 24

galad to see you algabraic

Answer 25

so close.

Answer 26

Wow, should I go now?
Btw, (1/t) (t^2) =/= 1/t^3,
(1/t)(t^2) = t

Answer 27

no thats not the answer

Answer 28

http://i.imgur.com/CMgMz.gif

Answer 29

I'm not saying that it is the answer, I haven't started differentiation yet..

Answer 30

\[(t-\frac{1}{t})(t^2-\frac{1}{t^2})\]\[=(t^3-t-\frac{1}{t}+\frac{1}{t^3})\]
So, \[\frac{d}{dt}(t-\frac{1}{t})(t^2-\frac{1}{t^2})\]\[=\frac{d}{dt}(t^3-t-\frac{1}{t}+\frac{1}{t^3})\]Use power rules, you can do it.

Answer 31

Sorry, it should be use the power rule :\

Answer 32

once again so close

Answer 33

You have to differentiate it yourself. That is not the answer.

Answer 34

i'm having trouble with the second halve

Answer 35

Which one?

Answer 36

i have 3t^2-1.......?

Answer 37

How did you get it?

Answer 38

the power rule

Answer 39

it is the answer but the rest is not adding up correctly

Answer 40

Power rule: d\dx (x^n) = nx^(n-1)

Answer 41

sorry make that simple differentiation

Answer 42

x^2 = 2x derivative

Answer 43

d\dx (x^2) = 2x => correct
What about d/dx (x^3) ?

Answer 44

x^3 = 3x^2

Answer 45

Yup, so what about d/dt (t^3) ?

Answer 46

my times up here i have to move on

Answer 47

thanks for confusing me

Answer 48

Sarcastic...
When you get that, you can differentiate it term by term, it shouldn't be difficult when you use the power rule. It would be even more terrible to use product rule.