Geometrically, there is a close relationship between the plots of and , they are reflections of each other over the line :
One may suspect that we can use the fact that , to deduce the derivative of . We will use implicit differentiation to exploit this relationship computationally.
From the derivative of the natural logarithm, we can deduce another fact:
We can also compute the derivative of an arbitrary exponential function.
2025-01-06 19:51:29