Solve for the Derivative of Inverse Function g

intenzxboi
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Homework Statement


Suppose that f has an inverse and f (6) = 18, f'(6) = 4/5. If g = 1/(f-1), what is g'(18)?

have no idea how to set up problem
 
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Do you read your textbook at all? If not then you should! In it you'll find a theorem that specifically deals with derivatives of inverse functions. Please flip through the section in which this exercise occurs and see if you can't find it. Then we can get started.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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