Question

Given y= f(t) = 2/t, find the derivative of y with respect to t.

Answer 1

the derivative of \(\frac{1}{x}\) is \(-\frac{1}{x^2}\) always

Answer 2

unless you are supposed to do this by hand

Answer 3

If \[
y=t^n\]
then
\[
y'= n t^{n-1}
\]

Answer 4

Apply the above for n=-1;

Answer 5

umm.
(2/t)^-1?
I think I am supposed to do this using the limit formula though.

Answer 6

that is what i suspected

Answer 7

this correct?

Answer 8

\[\frac{\frac{1}{t+h}-\frac{1}{t}}{h}\]

Answer 9

then a bunch of algebra,
subtract first up top

Answer 10

yes that is the formula.
@satellite73 i know the answer to this question so what you said earlier about 1/x makes sense.
I just don't know how to do this, and the teacher used the formula to solve this.

and ok,
2t-2(t+h)
----------
t(t+h)
?

Answer 11

sure looks good

Answer 12

numerator is just \(-2h\) when you distribute and combine like terms

Answer 13

so you are looking at \[\frac{-2h}{t(t+h)}\] now divide by \(h\)

Answer 14

-2h/th(t+h)
?

Answer 15

cancel the h top and bottom

Answer 16

gives \[\frac{-2}{t(t+h)}\] then put \(h=0\) to get the answer you know it has to be

Answer 17

ohhh.
oh i forgot about substituting.
ok.
-2/t(t+0)
= -2/t^2
thank you so much.

Answer 18

yw