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Mathematics 24 Online
OpenStudy (ujjwal):

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)

OpenStudy (anonymous):

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

OpenStudy (anonymous):

should be option d.

OpenStudy (anonymous):

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

OpenStudy (ujjwal):

It says, its option a P.S. I guess sth is wrong with the question! But may be i am wrong!

OpenStudy (anonymous):

but e^x should be in the answer!

OpenStudy (ujjwal):

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

OpenStudy (anonymous):

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

OpenStudy (ujjwal):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

@satellite73 how come?

OpenStudy (anonymous):

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

OpenStudy (amistre64):

say: cos(x) = u x = arccos(u) e^(arccos(u)) u

OpenStudy (anonymous):

maybe amistre knows

OpenStudy (anonymous):

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

OpenStudy (anonymous):

ooh is that how it works?

OpenStudy (amistre64):

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

OpenStudy (ujjwal):

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

OpenStudy (ujjwal):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

still lost i will shut up

OpenStudy (amistre64):

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

OpenStudy (anonymous):

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.

OpenStudy (ujjwal):

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

OpenStudy (anonymous):

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

OpenStudy (ujjwal):

Oh! yes.. I forget small things!

OpenStudy (anonymous):

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

OpenStudy (ujjwal):

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

OpenStudy (anonymous):

lol..yea!

OpenStudy (ujjwal):

Question closed! thanks everyone!

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