Explained that an injective function f:D-->R has an associated inverse function f-1:C-->D where C=f(D) is the range of f. Then gave a formula for the derivative of the inverse function. The function exp(x) or ex was introduced as the inverse of the natural logarithm function. The function f(x)=4x can be rigorously defined as the inverse to the function log4(x) = Ln(x)/Ln(4) .
Also defined the function y=sin-1(x) and then calculated its derivative.
See Section 3.5 in Stewart for more examples of derivatives of inverse functions.