# What is the derivative of this function #y=tan^-1(x^3)-x#?

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To find the derivative of the function ( y = \tan^{-1}(x^3) - x ), use the chain rule and the derivative of ( \tan^{-1}(x) ), which is ( \frac{1}{1+x^2} ).

First, find the derivative of ( \tan^{-1}(x^3) ): [ \frac{d}{dx}(\tan^{-1}(x^3)) = \frac{1}{1+(x^3)^2} \cdot 3x^2 ]

Then, find the derivative of ( -x ): [ \frac{d}{dx}(-x) = -1 ]

Combining these, the derivative of the function is: [ \frac{d}{dx}(y) = \frac{3x^2}{1+x^6} - 1 ]

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