Question

Find dy/dx
step by step? please? :)

Answer 1

\[y=ln(\frac{ x^4e^{3x} }{ \sqrt{2x^5-1} })\]

Answer 2

yuck!!!

Answer 3

I know ;(

Answer 4

i think it would be better to do logarithmic differentiation...

Answer 5

\(\large y=ln(\frac{x^4e^{3x}}{(2x-5)^{\frac{1}{2}}}) = 4lnx + 3x - \frac{1}{2}(2x^5-1)\)

simplifying y that way should be much simpler...

Answer 6

i guess that's not so hard afterall....

Answer 7

wait wait.. how'd you get 4ln(x)+3x-1/2(2x^5-1)

Answer 8

use the logaritm properties...

Answer 9

I need to look those up ;/ and review them.

Answer 10

\(\large ln(AB)=lnA+lnB \);
\(\large ln(A/B)=lnA-lnB \);
\(\large ln(A^B)=BlnA \);

hmm... i think that's all of 'em...

Answer 11

Awe, well thank you. Okay so now back to what you got.. Let me look over that real quick

Answer 12

yeah... should be easier now....

Answer 13

Okay so I see you used the second one.. But, I'm confused how you got those values...

ln(A)=4lnx+3x
when A= x^4e^{3x}

Answer 14

is it..ln(x^4)=4lnx

Answer 15

\(\large y=ln(\frac{x^4e^{3x}}{(2x-5)^{\frac{1}{2}}}) =ln(x^4e^{3x})-ln(2x-5)^{1/2} \)

Answer 16

that's the first step...

Answer 17

now....
\(\large ln(x^4e^{3x})=lnx^4+lne^{3x}=4lnx+3x \)
do u undestand this part?

Answer 18

ooo... sorry my bad... the second part is wrong....

Answer 19

ohhh... ln(A^b)=b*ln(A)

ln(x^4)=4*ln(x)
and e&ln cancel out leaving 3x

Answer 20

\(\large ln(2x-5)^{1/2}=\frac{1}{2}ln(2x-5) \)
that's what it should have been...

Answer 21

and yes (to your last post)

Answer 22

lemme rewrite what i shouldve written....

Answer 23

\(\large y=ln(\frac{x^4e^{3x}}{(2x-5)^{\frac{1}{2}}}) = 4lnx + 3x - \frac{1}{2}\color {red}{ln}(2x^5-1) \)

Answer 24

\[\frac{ 4 }{ x }+3..\]

Answer 25

yep... keep going...

Answer 26

I need to do chain rule?

Answer 27

yes, chain rule: \(\large [lny]'=\frac{y'}{y} \)

Answer 28

so \(\large [ln(2x^5-1)]'=\frac{[2x^5-1]'}{2x^5-1} \)
simplify....

Answer 29

\[\frac{ 4 }{ x }+3-\frac{ 1 }{ 2 }\frac{ 10x^4 }{ 2x^5-1 } = \frac{ 4 }{ x }+3-\frac{ 5x^4 }{ 2x^5-1 }\]

Answer 30

haha... looks good..:)

Answer 31

why haha? did I do something wrong?

Answer 32

no... i was getting the wrong answers until at the last moment when u posted ur answer... it confirmed my last answer...

Answer 33

oh lol :) you just discouraged me! >;[

no im jk ;) thank you!

Answer 34

oh wait...

Answer 35

haha... just kidding....
yw... :)

Answer 36

haha! jerk ;D

Answer 37

:)

Answer 38

i forgot...
nice work on your part... way to stick with the problem....

Answer 39

what you mean? I always finish ;D