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Derivatives of Inverse Functions - HELP!

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squance:
Hey. Im having issues with this question and would like some help.

Using implicit differentiation, show that..

d/dx(arccosec x) = -1/(x sqrt(x^2-1)), x>1

So far I have...

Let y = arccosec x

x = cosec y

d/dx(x) = d/dx(cosec y)
1 = d/dx(1/sin y)
1 = -cosy (dydx)/sin^2 y (after applying quoitent rule to 1/sin y)

I think i have to use the cos^2 y+ sin^2 y = 1 thing but I can't seem to get it.

Some help please?

Mao:




from this: ,







substituting the above expressions for sin y and cos y:



as required

squance:

--- Quote from: Mao on August 18, 2008, 06:47:22 pm ---




*typing*

--- End quote ---

Im not sure how you got 1=\frac{\sin y - \cos y}{\sin^2 y}\cdot \frac{dy}{dx} because i got -cos y (dy/dx)/ (sin^2(y)) using quotient rule....

Mao:
yeah, mistake :P fixed now

i forgot what was momentarily :P

squance:
Heheh
thanks for the help :)

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