Category 3: ArcSecant and ArcCosecant Please note you will also see these functi

Question

Category 3: ArcSecant and ArcCosecant
Please note you will also see these functions as ?sec?^(-1) or ?csc?^(-1)

1. Function: f(x)=arcsec?(8x) 3. Function: f(x)=arccsc?(9x)
Derivative: f^' (x)=8/(|8x| ?(64x^2-1)) Derivative: f^' (x)=-9/(|9x| ?(81x^2-1))


2. Function: f(x)=sec^(-1) (3x^5) 4. Function: f(x)=2csc^(-1) (x^6)
Derivative: f^' (x)= (15x^4)/(|3x^5 | ?(9x^10-1)) Derivative: f^' (x)=-(12x^5)/(|x^6 | ?(x^12-1))


What is the formula for the derivative of ArcSec? What about for ArcCsc?







Find the derivatives of the following:

1.f(x)=-2arcsec?(x^2) 2. f(x)=4arccsc?(2x^3)

Explanation / Answer

d(sec^-1 (x))/dx = 1/(|x|sqrt(x^2-1)) d(csc^-1 (x))/dx = - 1/(|x|sqrt(x^2-1)) 1. f'(x) = -2 * (2x/|x^2|sqrt(x^4-1)) f'(x)= -4x/|x^2|sqrt(x^4-1) 2. f'(x)=-4*(6x^2/|2x^3|sqrt(4x^6 - 1)) =-24x^2/|2x^3|sqrt( 4x^6-1)

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