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)

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




4.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:

2. 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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