Question

The derivative of \(e^x \cos x\) with respect to cosx is :
a)cosx - sinx
b)cosx+sinx
c)sinx-cosx
d)\(e^x\)(sinx+cosx)

Answer 1

i guess i do not understand what it means when you say "with respect to cosine"

Answer 2

should be option d.

Answer 3

@satellite73 it means instead of finding dy/dx....we have to find dy/d(cosx).

Answer 4

It says, its option a

P.S. I guess sth is wrong with the question! But may be i am wrong!

Answer 5

but e^x should be in the answer!

Answer 6

And that makes me think that something is wrong with qsn or answer!

Answer 7

i think so too....and the answer i got is e^x (1 - tanx).

Answer 8

Why is wolf not helping? http://www.wolframalpha.com/input/?i=differentiate+e%5Ex+cosx+with+respect+to+cosx

Answer 9

i guess it only does standard differentiation....ie, w.r.t x

Answer 10

oh sorry...i wrote the wrong answer before.
it should be e^x (1 - cotx)

Answer 11

if it is really wrt cosine, then it should be \(e^x\)

Answer 12

@satellite73 how come?

Answer 13

because it says "with respect to cosine"
unless you want to write cosines in terms of \(e^x\) using complex numbers
i guess i should be quiet because i am not really sure what "with respect to cosine" means in this case

Answer 14

say: cos(x) = u

x = arccos(u)

e^(arccos(u)) u

Answer 15

maybe amistre knows

Answer 16

dy/d(cosx) can also be written as
dy/dx the whole upon d cosx / dx.......now it is easier to solve.

Answer 17

ooh is that how it works?

Answer 18

i dunno if my method is right, but its just a hunch ... prolly wrong tho :)

Answer 19

I get this:\[-\frac{e^x(\cos x + \sin x)}{\cos^2 x \sin x}\]

Answer 20

Guys! This shouldn't be much complex! It doesn't fall in that category in my text book!

Answer 21

@satellite73 no!!
@ujjwal i know! and i'm telling u....i'm pretty confident about my answer.

Answer 22

still lost i will shut up

Answer 23

my idea gets me e^x(1-cotx)

Answer 24

let y = e^x * cos x
so dy/dx = e^x cosx - e^x sinx = e^x ( cosx - sinx).........(i)

now, d cosx/ dx = -sinx.............(ii)

now do (i) by (ii) to get the final answer.

Answer 25

You missed dividing by (e^x)^2 in eqn 1 @Vaidehi09

Answer 26

why do we have to do that?
the product rule says:
(uv)' = uv' + vu'

Answer 27

Oh! yes.. I forget small things!

Answer 28

so the answer is undoubtedly e^x ( 1 - cotx).

Answer 29

Yes! the answer is none of the given options! LOL...

Answer 30

lol..yea!

Answer 31

Question closed! thanks everyone!