Find derivatives via first principle using W|A?

Questions
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1

Hello,

I’d like to know if it is possible to limit the step-by-step solution to solely first principle, and if so, how would I go about searching for it via Wolfram Alpha?

Thank you in advance.

2

By first principles I suppose you mean the derivative rule theorems. Or do you mean the limit definition of the derivative? And if the limit, do you want the limit derived from the epsilon-delta definition or from the limit rule theorems? (All the possibilities seem like interesting exercises to automate.)

3

I’m looking for a way to automate something along these lines:

Find the derivative of f(x) = x² from first principles::

f’(x) = lim h->0 [f(x+h) - f(x)]/h

= lim h->0 [(x+h)² - x²)]/h

= lim h->0 [(x² + 2hx + h² - x²)]/h

= 2x

How would I type up a search query so that I could get step-by-step solutions such as those?

4

In Mathematica

deriv[funcofx_] := 
 Limit[ ((funcofx /. x -> x + h) - funcofx)/h, h -> 0]