## differentiation with inverse function

Limits, differentiation, related rates, integration, trig integrals, etc.

### differentiation with inverse function

If $f(x) = (2x-\pi)^3+2x-cosx$.Then Calculate $\displaystyle\frac{d}{dx}\left(f^{-1}(x)\right)$ at $x=\pi$
stuart clark

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Joined: Wed Jan 19, 2011 7:11 am

### Re: differentiation with inverse function

stuart clark wrote:If $f(x) = (2x-\pi)^3+2x-cosx$.Then Calculate $\displaystyle\frac{d}{dx}\left(f^{-1}(x)\right)$ at $x=\pi$

The first step will be to find the value $a$ for which $f(a)\, =\, \pi$, since then $f^{-1}(\pi)\,=\,a$. Hint: Consider values for which the cosine will be zero.

Then use the fact that $\left[f^{-1}(\pi)\right] = \frac{1}{f'(f^{-1}(\pi))}$, plugging in the value you have found for $a\, =\, f^{-1}(\pi)$.
nona.m.nona

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Joined: Sun Dec 14, 2008 11:07 pm