Question

Derivative of (3/(5t)-1)/((2/t^2)+7)?

Answer in the book is:
(-21t^2 - 20t + 6)/(5(2 + 7t^2)^2

I don't know what is going on with my math, but I can't seem to get this right :[

Here are my fail attempts :
1. http://puu.sh/4FyMW.JPG
2. http://puu.sh/4FyTA.JPG

Answer 1

you cannot multiply and divide by different quantities (5t and t^2)

start by multiplying and dividing by 5t^2

Answer 2

yeah i knew that, but i tried it anyways to see what would happen haha.
but in the 1st picture, i felt like i was on the right track, but i don't know anymore

Answer 3

in 1st pic , you took the derivative of numerator and denominator separately ? instead of using quotient rule ? thats not allowed

Answer 4

yes, don't you need the derivative of the numerator and denominator to use the quotient rule?

Answer 5

let me check again

Answer 6

(3/5*t^(-1)-1)/(2t^(-2)+7)
d(u/v)/dt=(u'v-v'u)/v^2
u'v=-1(3/5)t^(-2)*v
uv'=-4t^(-3)*u
That should get you started.

Answer 7

mmk i'm gonna try that

Answer 8

easier thing to do is to multiply and divide by 5t^2

Answer 9

i'm making this so complicated for myself :(
i'll try what you said by multiplying and dividing by 5t^2 instead

Answer 10

sorry that took so long. for some reason, the 5's cancelled out at the end

Answer 11

http://puu.sh/4Fzw0.JPG

Answer 12

oh nvm, i see the problem. oops~ thx guys :D

Answer 13

oh, so you got it now ?

Answer 14

yeah. too tired to think at this time. i'm not noticing all these little things

Answer 15

\((10+35t^2)=5^2(2+7t^2)^2\)

Answer 16

thats where the error lies

Answer 17

you have only written 5(....)^2

Answer 18

eheh. can't believe i spent 41 mins on a one math problems :(

Answer 19

if its any consolation, i have, many times spent 7-8 hours on one problem :P

Answer 20

lol xD. good night! i think i need it

Answer 21

sure, have a sound sleep and sweet dreams :)