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|

?81^2-1


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:

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

Explanation / Answer

1/|x|sqrt[x*x - 1] for cosec inverse : -1/|x|sqrt[x*X - 1] 2) -4/xsqrt[x^4 - 1] -(3/4)/xsqrt[4x^6 - 1]

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