`x^2 + xarctany = y - 1 , (-pi/4, 1)` Use implicit differentiation to find an equation of the tangent line at the given point

Does the given point belongs to the given curve?

`x^2 + x arctany = pi^2/16 - pi/4*pi/4 = 0,` and `y - 1 = 0` also.

Then equation of the tangent line is `(y - 1) = (x + pi/4)*y'(-pi/4).` Perform implicit differentiation to find `y':`

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

solve this equation for `y':`

`y'(x) = (2x + arctany)/(1-x/(1+y^2)).`

At the given point it is equal to `-(2pi)/(8+pi),` and the equation of the tangent line is

`y = 1 - (x + pi/4)*(2 pi)/(8+pi).`

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