Question

What is the slope of the tangent line to y=xarctan x at x=1?

Answer 1

I need help taking the derivative of y = xarctanx I can't get a nice answer.

Answer 2

I used product rule to get:
dy/dx = arctanx + d/dx(arctanx)*x

Answer 3

Tell me if I'm doing this right:
arctanx = y
tany = x
sec^2(y) dy/dx = 1
dy/dx = cos^2(y)
dy/dx = 1 - x^2

Answer 4

Using this

Answer 5

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