Why doesn't count as an "inside" function?
Here we see an example of the chain rule. Derivative of the inside function times the derivative of the outside function...
However, with this example:
There is no derivative of the inside and then outside. It seems to adhere to normal differentiation rules such as:
Why is this? Thanks!
Uuhhh... it depends on what we are talking about... is a single 1 dimensional number a function ? I don't know. In 2 dimensions f(x) = c is a function , it is a horizontal line that takes on all x values exactly once and every x value has only 1 y value and therefore passes the so called 'vertical line test'. Similarly f(x) = ln 7 is a function in 2 (or more) dimensions. For any real number c , one may decide to rewrite this as
In order to have a 'place' to sbstitute for x ... this works out fine for all real x EXCEPT x = 0 where we encounter the 'disagreeable'
Personally, it doesn't bother me too much and i won't throw it away just because there is a problem at x = 0 , but that's me , others may disagree.