Find the derivative of the function. Simplify if possible. `y = tan^(-1) x^2`

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lemjay | High School Teacher | (Level 3) Senior Educator

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`y = tan^(-1) x^2`

To determine the derivative of y,  use the formula  `(tan ^(-1) u)' = 1/(1+u^2) * u'` .

`y ' = 1/(1+ (x^2)^2) * (x^2)' = 1/(1+x^4) * 2x`

`y ' = (2x)/(1+x^4)`

Hence, the derivative of `y = tan^(-1) x^2` is `y' = (2x)/(1+x^4)` .

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