I try to get the step-by-step solution for D[E^x, x] as follows:
WolframAlpha["D[E^x, x]", IncludePods -> "Input",
AppearanceElements -> {"Pods"}, PodStates -> {"Input__Show steps"}]
The result is given below:
As you can see, this proof method is clearly trapped in the logic of circular argumentation, and therefore invalid.
Regards,
Zhao
It is not circular. It shows that if you know the derivative at x = 0 then you know it at any generic x. The derivative at x = 0 is a limit that is treated in all serious calculus textbooks. Do you expect W|A to give you all the steps up to the axioms of the real numbers?
Do you expect W|A to give you all the steps up to the axioms of the
real numbers?
Is this possible?
I think that in this case W|A has given a pretty reasonable answer in this case. The limit Limit[(E^x - 1)/x, x -> 0]==1 is basic in every calculus textbook that I know of.
If you ask W|A the steps for the limit Limit[(E^x - 1)/x, x -> 0], it uses L’Hôpital’s rule, which assumes that we know the derivative of the exponential. This would have been circular!
