Category 2: ArcTangent and ArcCotangent Please note you will also see these func

Question

Category 2: ArcTangent and ArcCotangent
Please note you will also see these functions as ?tan?^(-1) or ?cot?^(-1)

1. Function: f(x)=arctan?(3x) 3. Function: f(x)=7tan^(-1)?(x^2)
Derivative: f^' (x)=3/(1+9x^2 ) Derivative: f^' (x)=14x/(1+x^4 )


2.Function: f(x)=arccot?(6x) 4. Function: f(x)=1/3 cot^(-1) (2x^3)
Derivative: f^' (x)=-6/(1+36x^2 ) Derivative: f^' (x)=-(6x^2)/(3(1+4x^6))




What is the formula for the derivative of ArcTan? What about for ArcCot?







Find the derivatives of the following:

1.f(x)=1/2 arctan?(x^4) 2. f(x)=6arccot?(7x^3)

Explanation / Answer

2x^3/[1 + x^8] -132x^2/[1 + 49x^6]

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