Why does xcosx simplify down to cosx-xsinx ?

Question

anonymous · Answer

wowee. i am going to assume you mean 
"why is the derivative of 
$$f(x)=x\cos(x)$$
$$f'(x)=\cos(x)-x\sin(x)$$"

anonymous · Answer

integration?

amistre64 · Answer

im assuming by simplify you mean integrates into

anonymous · Answer

yes, that's what i meant satellite73

anonymous · Answer

finding a derivative is by no means the same thing as "simplifying"

amistre64 · Answer

lol ... :)  the derivative wins

anonymous · Answer

could you please explain how it simplifies to that

anonymous · Answer

or derives

amistre64 · Answer

it doesnt simplify to that ....

amistre64 · Answer

if anything it transforms into that, complicates into that, morphs into that .... by no means does it simplify into it

amistre64 · Answer

as the limit definition will attest to

anonymous · Answer

a term that should be washed out of every idiot math teachers mouth
ok done ranting.  use the "product rule"
$$(fg)'=f'g+g'f$$
with 
$$f(x)=x,f'(x)=1,g(x)=\cos(x), f'(x)=-\sin(x)$$ ad you will get it in one step

amistre64 · Answer

the product rule aint the "why" tho

amistre64 · Answer

a guy pulls a rabbit out of a hat, why?  because he stuck his hand in the hat and pulled out a rabbit lol

anonymous · Answer

i am making an assumption that the question is asking "what is the derivative of 
$$F(x)=x\cos(x)$$ rather than what was actually asked.  in other words i assume that the "why" meant "how do i get"

anonymous · Answer

ok i got it thank you, thus using the product rule you can derive it to that.

anonymous · Answer

btw i hope you know to write 
$$\cos(x)$$ rather than the common but hideous 
$$\cos x$$ it will save a lot of confusion when doing such problems

anonymous · Answer

morphs .  i like "it morphs into that"

amistre64 · Answer

my math teacher didnt give me the extra credit points; simply because I used IBP instead of a u-substitution.  SHe said it was becasue she hasnt taught us that yet.

amistre64 · Answer

just call me morpheus lol

anonymous · Answer

ibp??

anonymous · Answer

oh right

amistre64 · Answer

integration by parts

amistre64 · Answer

so much for teachers encouraging initiative these days

anonymous · Answer

heaven forbid you should know something right? meanwhile they all say "read ahead in the book, come prepared for class..."

anonymous · Answer

but know only what i tell you.  0 is a natural number because i said so.

amistre64 · Answer

:)