not sure what you're after here, but if u and v are functions of x, then
d/dx u^v = v u^(v-1) v' + lnu u^v u'
Now use that and the product rule to find f'(x), if that's what you need.
f ' (0) f(x)= [ x^2(cosx)^cotx, x is not 0 ]
[ 0 , x=0 ]
6 answers
sorry can you give me more information?
*sigh*
d/dx x^2(cosx)^cotx = 2x (cosx)^cotx + x^2 (v u^(v-1) v' + lnu u^v u')
where u = cosx and v = cotx
maybe you can give me some more information. All that mumbo jumbo you wrote isn't very clear.
d/dx x^2(cosx)^cotx = 2x (cosx)^cotx + x^2 (v u^(v-1) v' + lnu u^v u')
where u = cosx and v = cotx
maybe you can give me some more information. All that mumbo jumbo you wrote isn't very clear.
f ' (0) for the function f(x)= { x^2(cosx)^cotx, x is not 0 }
{ 0 , x=0 }
And can I ask that why the website said that more foul language or rude behavior is detected......
I never said any badword before
{ 0 , x=0 }
And can I ask that why the website said that more foul language or rude behavior is detected......
I never said any badword before
When teacher oobleck said
mumbo jumbo he was trying to tell you that he doesn't understand the way you presented your question
Look what I did
And let obleck confirm more for you
F(x)=x^2(cosx)^cotx
Using product rule
U=x². V=(cosx)^cotx
U'=2x
V=(cosx)^cotx
lnv=cotx.lncos(x)
(I/v)v'=[uv'+vu'={(-sinx/cosx(cotx)-lncos(x)cosec²x}=sinx/cosx(cosx/sinx)+lncosx(cosec²x)=
V'(x)=-cosx^(cotx)lncosxcosec²x
F'(x)=uv'+vu'=-x²cosx^(cotx)(lncos(x)cosec²x+cosx^(cotx)2x
=xcos(x)^(cotx)[2-cosec²x.lncos(x)]
mumbo jumbo he was trying to tell you that he doesn't understand the way you presented your question
Look what I did
And let obleck confirm more for you
F(x)=x^2(cosx)^cotx
Using product rule
U=x². V=(cosx)^cotx
U'=2x
V=(cosx)^cotx
lnv=cotx.lncos(x)
(I/v)v'=[uv'+vu'={(-sinx/cosx(cotx)-lncos(x)cosec²x}=sinx/cosx(cosx/sinx)+lncosx(cosec²x)=
V'(x)=-cosx^(cotx)lncosxcosec²x
F'(x)=uv'+vu'=-x²cosx^(cotx)(lncos(x)cosec²x+cosx^(cotx)2x
=xcos(x)^(cotx)[2-cosec²x.lncos(x)]
The simplified form of the last part
I omitted 'x'
But this is it
=xcos(x)^(cotx)[2-xcosec²x.lncos(x)]
I omitted 'x'
But this is it
=xcos(x)^(cotx)[2-xcosec²x.lncos(x)]