Implicit differentiation and inverse trigonometric functions practice question 14

To find an intercept of the tangent line you first need the line: a point and a slope at $x = 1$. Which rule does the slope of $x\arctan x$ need?

Product rule: the derivative of $x\arctan x$ is $\arctan x + \dfrac{x}{1 + x^{2}}$. Evaluate it, and the curve, at $x = 1$.

Write the tangent line as $y = f(1) + f'(1)(x - 1)$, set $y = 0$, and solve for $x$.