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can someone derive f(x) = x using first principles method. Like I know the answer is 1 and can do it by power rule but i cannot get that answer for the life of me using first principles method.

fyi first principles function is in the pic

can someone derive fx x using first principles method Like I know the answer is 1 and can do it by power rule but i cannot get that answer for the life of me us class=

Respuesta :

The derivation by definition of f(x) = x, that is, f'(x) = 1, is found in this problem.

How to find the derivative of function f(x) by the definition?

The derivative is given by:

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h}[/tex]

For this problem, we have that:

  • f(x) = x.
  • f(x + h) = x + h.

Hence:

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} \frac{x + h - x}{h}[/tex]

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} \frac{h}{h}[/tex]

[tex]f^{\prime}(x) = \lim_{h \rightarrow 0} 1[/tex]

The limit of a constant is the constant, hence f'(x) = 1.

More can be learned about derivatives by definition at https://brainly.com/question/23819325

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