I could not solve this for quite sometime...
lets see who can ...
let f(x)=(2x-Ï€)3 + 2x - cos x
find ddx[f-1(x)] at x=Ï€ [1][1][1]
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3 Answers
venkateshan
·2010-09-07 09:25:45
hey subho.....
just check out this link 4 da solution......
http://www.targetiit.com/iit-jee-forum/posts/differentiation-2-17388.html
i had also asked the same doubt earlier.....
bindaas
·2010-09-07 11:12:04
f(a)=Ï€
x=Ï€2
f'(Ï€2)=3
now use
f^{-1}(f(x))=x \\ \frac{d }{d x}{f^{-1}(f(x))}=1\\ \texttt{apply chain rule} \\ \frac{d }{d x}{f^{-1}(f(a))}=\frac{1}{f'(a)}
\frac{d }{d x}{f^{-1}(\pi)}=\frac{1}{3}
Subhomoy Bakshi
·2010-09-07 11:37:22
no i have solved this now...
just gave this as i found the question fascinating!
neways thanks! :)