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This question already has an answer here:

What is derivative of $\sin\sqrt x$ using the definition of the derivative ?

The definition of derivative is:-

$$\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$$

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marked as duplicate by Jimmy R., Clarinetist, Community Dec 21 '16 at 14:49

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Are you allowed to use Taylor series? $\endgroup$ – Clarinetist Dec 21 '16 at 14:37
  • $\begingroup$ This is kind of unmotivated. Is this a homework problem? What have you tried? $\endgroup$ – Callus Dec 21 '16 at 14:37
  • $\begingroup$ Really? First principles? Why? Why would anyone want to do that, to himself or to his students? Really... $\endgroup$ – DonAntonio Dec 21 '16 at 14:37
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    $\begingroup$ math.stackexchange.com/questions/1629163/… $\endgroup$ – Jimmy R. Dec 21 '16 at 14:38
  • $\begingroup$ Not a good exercise because you have to use the same steps used for proving the chain rule. $\endgroup$ – user384138 Dec 21 '16 at 14:40