Question

find the 2nd derivitave of sinx/3+cos2x
but please show me the first step !!

Answer 1

\[\frac{\sin(x)}{3+\cos(2x)} ?\]

Answer 2

ye

Answer 3

whats my first step?? like im having trouble with the 3

Answer 4

my first step i got is cosx (3+cos2x) - sin(-sin2x)(s)/ (3+cos2x)^2

Answer 5

The following is the first derivative
I applied the quotient rule because we had a quotient
\[\frac{(\sin(x))' \cdot (3+\cos(2x)-(\sin(x)) \cdot (3+\cos(2x))'}{(3+\cos(2x))^2}\]

Answer 6

\[\frac{\cos(x) \cdot (3+\cos(2x))-\sin(x) \cdot (0-2\sin(2x))}{(3+\cos(2x))^2}\]

Answer 7

so i was right?

Answer 8

kinda

Answer 9

some of what you wrote is right

Answer 10

ok, ill just ask my teacher tomo, cause this is a long question :p

Answer 11

aww...you don't understand what I did?

Answer 12

well, i did, but i need to find 2nd derivative and thats gonna take a loooong time :p

Answer 13

\[\frac{\cos(x)(3+\cos(2x))+2\sin(2x)\sin(x)}{(3+\cos(2x))^2}\]
\[\frac{3\cos(x)+\cos(2x)\cos(x)+2\sin(2x)\sin(x)}{(3+\cos(2x))^2}\]
-------------
Now second derivative
Again we need to do quotient rule

Answer 14

..............
how did u do the 2nd part???

Answer 15

lol It is too long to fit on one line
one sec

Answer 16

Gosh I can't make it look pretty on here.
You have to apply quotient rule first

Answer 17

Then you will have to use product rule a couple of times

Answer 18

and chain rule too

Answer 19

How about this we do it in small parts

Answer 20

its okay man
its alot of work :) ill do it tomo with my teacher, dont waste your time

Answer 21

\[(\frac{3\cos(x)+\cos(2x)\cos(x)+2\sin(2x)\sin(x)}{(3+\cos(2x))^2})'\]
\[=\frac{(3\cos(x)+\cos(2x)\cos(x)+2\sin(2x)\sin(x))'(3+\cos(2x))^2}{(3+\cos(2x))^4} \]
\[-\frac{(3\cos(x)+\cos(2x)\cos(x)+2\sin(2x)\sin(x))((3+\cos(2x))^2)'}{(3+\cos(2x))^4}\]

Answer 22

Couldn't put it all on one line
So we need to find this:
\[(3\cos(x)+\cos(2x)\cos(x)+2\sin(2x)\sin(x))'\]
and
\[((3+\cos(2x))^2)'\]

Answer 23

\[(3\cos(x)+\cos(2x)\cos(x)+2\sin(2x)\sin(x))'\]
\[=-3\sin(x)+(-2\sin(2x)\cos(x)+\cos(2x)(-\sin(x))+2(2\cos(2x)\sin(x) \]
\[+\sin(2x)(\cos(x))\]

Answer 24

\[((3+\cos(2x))^2)'=2(3+\cos(2x))(0-2\sin(2x))\]
Now just plug in these parts :)

Answer 25

You might want to simplify too if possible