Question

dy/dt of y=(ln(2t))/(5t)

Answer 1

y = a/b ; y' = (ba' - ab')/b^2

Answer 2

Yes I know it's the quotient rule but somewhere I am messing up... can't find my error

Answer 3

I get ((ln(2t)*5)-((1/2t)*2)(5t))/(5t^2) which is incorrect, sorry for all the parenthesis it's how I have to enter it on on the website haha

Answer 4

trying denominator*(derivative of numerator) - (numerator)*derivative of denominator

Answer 5

Yeah I understand that I'm just messing up somewhere I suppose... Can't find it though it's really frustrating!

Answer 6

deriv of ln(2t) = (1/2t)*2 right?

Answer 7

yes

Answer 8

Idk then.. my answer looks 100% right to me but it isn't! :(

Answer 9

i got (1-ln2t)/5t^2. is that right?

Answer 10

Nope sadly

Answer 11

\(\large\color{black}{ \displaystyle y=\frac{\ln(2t) }{5t} }\)

\(\large\color{black}{ \displaystyle \frac{dy}{dt}=\frac{\frac{1}{t}(5t)+5\ln(2t) }{(5t)^2} }\)

\(\large\color{black}{ \displaystyle \frac{dy}{dt}=\frac{5+5\ln(2t) }{25t^2} }\)

\(\large\color{black}{ \displaystyle \frac{dy}{dt}=\frac{1+\ln(2t) }{5t^2} }\)

Answer 12

firstly the way you started is incorrect
you must abide the order when you do the quotien rule unlike the product rule where you can start with any

Answer 13

I differnetiated the top function, except I wrote the + instead of -

Answer 14

\(\large\color{black}{ \displaystyle \frac{dy}{dt}=\frac{1-\ln(2t) }{5t^2} }\)

Answer 15

thats what i got

Answer 16

F(x)/G(x) = { F`(x) G(x) - F(x)G`(x) } / G^2(x)

Answer 17

@ineptAtMath yes your answer is correct

Answer 18

Okay you were right ineptatMath. I needed to add a parenthesis

Answer 19

and why is derivative of any ln(Ct) with respect to t is 1/t
\(\large\color{black}{ \displaystyle (~\ln(Cx)~)'=\frac{1}{Cx}\times C }\)
or
\(\large\color{black}{ \displaystyle (~\ln(Cx)~)'=(~\ln(x)+\ln(C)~)'=\frac{1}{x}+0=\frac{1}{x} }\)

Answer 20

So in ln(Cx) (had a typo in the beginning) is just a vertical shift of ln(x) , C units up

Answer 21

(1-ln2t) needed to be (1-ln(2t)) lol

Answer 22

Thanks for the explanation and help guys! Going to go over what you've sent so I can see what I did wrong

Answer 23

;)

Answer 24

Oh sorry about that!

Answer 25

abt what /

Answer 26

?

Answer 27

the lack of parenthesis in what i wrote was confusing

Answer 28

oh, if you write a space, it is most fine, but yes, don't leave your parenthesis out, becuase not everyone will see the typo behind it.

Answer 29

I hand-written my essay once, and my "second" looked like "secont" (in 8th grade)
And that brought my paper from 98 to 93.

Answer 30

duly noted! ^^ And omg..... just one misspelled word dropped you down 5%? Harsh

Answer 31

no, for that mistake in 8th grade, it is just like not knowing what integral is in calculus 2.

Answer 32

it is not as low level mistake to assume a typo, but not as high to go over...

Answer 33

anyway.... \(\Huge\bf\rlap{\color{red}{G\ o\!}}{\color{blue}{\; {G\ o\ }}}\)\(\Huge\bf\rlap{\color{red}{o\ d\ }}{\color{blue}{\; {o\ d\ }}}\) \(\Huge\bf\rlap{\color{red}{L\ u\!}}{\color{blue}{\; {L\ u\ }}}\)\(\Huge\bf\rlap{\color{red}{c\ k\ }}{\color{blue}{\; {c\ k\ }}}\) \(\Huge\bf\rlap{\color{red}{~!}}{\color{blue}{\; ~{!}}}\)

Answer 34

Haha okay! Good luck to you too :)