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

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Expert Answers

hkj1385 | Certified Educator

*Note:- 1) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = real number*

*2) If y = tan^(-1)x ; the*

*dy/dx = 1/{1 + (x^2)}*

Now, the given function contains sub-functions, so the chain rule of differentiation is to be followed

Thus,

y = {tan^(-1)x}^2

Differentiating both sides w.r.t 'x' we get

dy/dx = 2*{tan^(-1)x}*[*1/{1 + (x^2)}]*

*or, dy/dx = 2[tan^(-1)x]/[ 1 + (x^2)]*