Question

Differential operator

Answer 1

D ( x cosx) = x (-sinx) + cosx = -x sinx + cosx
D ( -x sinx + cosx) = D(-x sinx) + D(cosx) = -x cosx - sinx - sinx = -x cosx -2 sinx

Answer 2

It has 2D^2. First, I took the first and second derivative of xcosx then i multiplied it with 2. Am i right?

Answer 3

once you have D and D^2 (see above) , yes you multiply and combine.
But I am guessing your D^2 has only 1 sinx (rather than 2sinx)

Answer 4

yes. 1sinx only.. Then why is it -4sinx? hehe

Answer 5

because D^2 (x cosx) = -x cosx -2 sinx
(I posted how to get this up above)

Answer 6

Omg Hahha im so stupid. I forgot the derivative of cosx. hahah Thank you so much. Thank you.. Can you help me again? regarding this topic again?

Answer 7

I can try

Answer 8

Heres my first second and third derivative of lncosx and 2 tanx

Answer 9

for lncosx = 1. -tanx. 2. -sec^2x 3. -2sec^xtanx

Answer 10

for 2tanx 1. 2sec^2x 2. 4sec^2xtanx 3. 4sec^4x + 8sec^2xtan^2x

Answer 11

typo on 3. for ln cosx

Answer 12

Ah yes haha -2sec^2xtanx

Answer 13

it all looks good.

Answer 14

My answer isnt the same with the correct one. Haha I got -8sec^4x+16sec^2xtan^2x. So wrong

Answer 15

first, did you account for the minus sign in -2 tanx (I see you found D, etc for 2 tanx)

Answer 16

the +1 in (2D^3 -D^2 +1) should give us ln cosx - 2 tanx
and so you should at least have the ln cosx term in the final answer.

Answer 17

Yes. Wait. Ill put my whole solution here. hehe

Answer 18

your answer has no secants, so maybe they used
sec^2 x - 1 = tan^2 x
to remove them

Answer 19

replace your sec^2 with tan^2 + 1
and simplify, and you will get their version

Answer 20

I think I would "define" (using your results posted above)
D^3 = -2sec^2xtanx - 4sec^4x - 8sec^2xtan^2x
D^2 = -sec^2x - 4sec^2xtanx

now combine 3D^3 -D^1 + lncosx -2tanx

Answer 21

now combine 2D^3 -D^1 + lncosx -2tanx

Answer 22

2 ( -2sec^2xtanx - 4sec^4x - 8sec^2xtan^2x )
-1 ( -sec^2x - 4sec^2xtanx)
+ lncosx -2tanx

Answer 23

you get (leaving out the argument x)
-4 sec^2 tan -8sec^4 -16sec^2tan^2
+sec^2 +4sec^2tan
+ lncosx -2tanx

Answer 24

yes

Answer 25

cancelled 4sec^2xtanx and -4blabla

Answer 26

-8sec^4 -16sec^2tan^2 +sec^2 + lncosx -2tanx
-8(tan^2 +1)^2 -16(tan^2 +1)tan^2 +(tan^2 +1) + lncosx -2tanx

Answer 27

Ah with tan^2-1

Answer 28

tan^2+1)^2.. Tan^4 + 2tan^2 + 1

Answer 29

-8tan^4 -16tan^2 - 8 -16tan^4 -16tan^2 +tan^2 +1 +lncosx-2tanx

Answer 30

yes, now combine like terms to get
-24 tan^4 -31 tan^2 + lncos -2tan -7

Answer 31

Yes thank you so much @phi =)