Find the slope of the line tangent to the graph of y = tan^−1 x at x= −2.

Verified step by step guidance

1. Identify the function for which you need to find the tangent slope: y = tan^−1(x).
2. Differentiate the function y = tan^−1(x) with respect to x to find the derivative, which represents the slope of the tangent line.
3. Recall the derivative of the inverse tangent function: dy/dx = 1 / (1 + x^2).
4. Substitute x = -2 into the derivative to find the slope at that specific point.
5. Simplify the expression obtained from the substitution to determine the slope of the tangent line at x = -2.