Category 1: ArcSine and ArcCosine Please Note you will also see these functions

Question

Category 1: ArcSine and ArcCosine
Please Note you will also see these functions as sin^(-1) or cos^(-1)

1.Function: f(x)=arcsin(2x) 2. Function: f(x)=3sin^-1(x^2)
Derivative: f^' (x)=2/1-4x^2 Derivative: f^' (x)=6x/1-x^4




3.Function: f(x)=cos(5x) 4. Function: f(x)=cos^(-1) (x^3)
Derivative: f^' (x)=-5/(1-25x^2 ) Derivative: f^' (x)=-(3x^2)/(1-x^6 )


What is the formula for the derivative of ArcSine? What about for ArcCosine?







Find the derivatives of the following:

1. f(x)=2arcsin(3x) 2. f(x)=-arccos(5x^2)

Explanation / Answer

6/sqrt[1 - 9x*x] 10x/sqrt[1 - 25x^4]

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