Implicit Diff with arctan (5.7 p 380 #71) Here we find a tangent line of a function using implicit differentiation, the product rule, the chain rule, and some careful algebra.
The Derivative of an Inverse Function (5.3 p340 #67) The derivative of a inverse function is the reciprocal of the derivative of the inverse function. Be mindful of the exchange of values (x,y) to (y,x) with inverse functions