Question

Im getting confused with this::::

find the derivative of:

r = 2/s^3 - 5/s

Answer 1

\[the derivative = 2x ^{-3}-5x ^{-1}\]

Answer 2

an then you do this to derive it....

Answer 3

\[derivative= -6x+5x ^{-2}\]

Answer 4

the above is your answer

Answer 5

or you can write the answer like this...

Answer 6

\[derivative = -6x+(5/x ^{2})\]

Answer 7

Fan me if that helped :D

Answer 8

why does the 5/s change to 5s^-1?? can you please tell me how to change

Answer 9

There is a rule with derivatives that says that if there is for example 5/s then you can write it as well as 5s^-1

Answer 10

other examples are 288/x^7 = 288x^-7

Answer 11

IF 5/s if equal to 5s^-1 then why is it 5s^-2??

Answer 12

actually, its the rules of exponents.
So when you have
\[X ^{-a} = 1/(X ^{a})\]

Answer 13

the negative sign represents the inverse.

Answer 14

What I did there was following that rule where you multiply the exponent by the coefficient.
so what I did was get =2x^(−3)−5x^(−1) using the rule of exponents. Then I multiplied the 2 in front of the x by the x's exponent (2X(-3)) = -6
then I subtracted 1 from the exponent -> (-3-1)= -4

Answer 15

wow I just realised that I made a mistake

Answer 16

the final answer should be -6x^(-4)+5x^(-2)

Answer 17

sorry about that

Answer 18

yeah so like I was saying before you subtract 1 from the exponents

Answer 19

the final answer in the ANSWERS SHEET IS
\[-6/s^{4} + 5/s^{2}\]

Answer 20

in replying to your question above,
\[r=(2/s ^{3}) - (5/s)\]
\[r= 2s ^{-3} - 5s ^{-1}\]
Find the derivative
\[r'= (-3)(2s ^{-3-1}) - (-1)(5s ^{-1-1})\]
\[r' = -6s ^{-4} + 5s ^{-2}\]

Answer 21

thank you heaps... that is great ~ i can actually see what is happening :)

Answer 22

no problem. calculus is very easy if you just follow all the rules properly =)

Answer 23

do u no a good website where i can learn calculus quickly?

Answer 24

Calculus is actually something best learned in the setting of a classroom. But if you have any questions to ask just ask here and ill be more than happy to assist you.

Answer 25

great thanks heaps :)

Answer 26

yup