Question

help with finding derivative

Answer 1

ok what is the problem

Answer 2

given y=\[\ln((\sqrt{\sin \theta \cos \theta})/(1+2\ln \theta)) \]

find \[dy/d \theta\]

Answer 3

\[y=\ln(\frac{\sqrt{\sin(\theta)*\cos(\theta)}}{1+2\ln(\theta)})\]
right?

Answer 4

given y=\[\ln((\sqrt{\sin \theta \cos \theta})/(1+2\ln \theta)) \]

find \[dy/d \theta\]

Answer 5

yes

Answer 6

ok cool
so you remember ln(a/b)=lna-lnb?

Answer 7

given y=\[\ln((\sqrt{\sin \theta \cos \theta})/(1+2\ln \theta)) \]

find \[dy/d \theta\]

Answer 8

yes

Answer 9

given y=\[\ln((\sqrt{\sin \theta \cos \theta})/(1+2\ln \theta)) \]

find \[dy/d \theta\]

Answer 10

for some reason my problem keeps getting posted again

Answer 11

\[y=\ln(\sqrt{\sin(\theta)*\cos(\theta)})-\ln(1+2\ln(\theta)\]

Answer 12

testing 123

Answer 13

okay

Answer 14

\[y=\frac{1}{2}*\ln(\sin(\theta)*\cos(\theta))-\ln(1+2\ln(\theta))\]
good so far?

Answer 15

yes its good

Answer 16

now if we take derivative of both sides we get:
\[\frac{y'}{y}=\frac{1}{2}*\frac{\cos(\theta)*\cos(\theta)+\sin(\theta)*(-\sin(\theta))}{\sin(\theta)\cos(\theta)}-\frac{2\frac{1}{\theta}}{1+2\ln(\theta)}\]

Answer 17

hmm

Answer 18

okay i see that

Answer 19

to find derivative of ln(sin(theta)*cos(theta))
we have to do (sin(theta)*cos(theta))'/(sin(theta)*cos(theta))
but to find the derivative of a product we have to use the product rule
correct?

Answer 20

yes

Answer 21

now to find y' what is the last step?

Answer 22

multiply both sides by y

Answer 23

yes!

Answer 24

wait oops that y is not suppose to be there i'm sorry

Answer 25

multiply both sides by y

Answer 26

oh no

Answer 27

its suppse to be y'=all of that
not
y'/y=all of that
sorry

Answer 28

so, dont multiply both sides by y

Answer 29

no you are already dont because you never had y'/y
you just had y'

Answer 30

can you show me what the solution would look like? tk

Answer 31

if would be what i have just ignore the y at the bottom of y' k?

Answer 32

okay thanks

Answer 33

\[y'=\frac{1}{2}*\frac{\cos(\theta)*\cos(\theta)+\sin(\theta)*(-\sin(\theta))}{\sin(\theta)\cos(\theta)}-\frac{2\frac{1}{\theta}}{1+2\ln(\theta)}

Answer 34

\[y'=\frac{1}{2}*\frac{\cos(\theta)*\cos(\theta)+\sin(\theta)*(-\sin(\theta))}{\sin(\theta)\cos(\theta)}-\frac{2\frac{1}{\theta}}{1+2\ln(\theta)} \]

Answer 35

alright, ty, u r the best

Answer 36

:)