Difference between revisions of "Derivative"

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Let $X$ be a subset of [[real number|real numbers]], $x_0 \in X$, and let $f \colon X \rightarrow \mathbb{R}$ be a function. We say that $f$ is differentiable at $x_0$ if the [[limit]]
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Let $D$ be a subset of [[complex number|complex numbers]], $z_0 \in D$, and let $f \colon D \rightarrow \mathbb{C}$ be a [[function]]. We say that $f$ is (complex-) differentiable at $z_0$ if the [[limit]]
$$f'(x_0)=\displaystyle\lim_{h \rightarrow 0} \dfrac{f(x_0+h)-f(x_0)}{h}$$
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$$f'(z_0)=\displaystyle\lim_{h \rightarrow 0} \dfrac{f(z_0+h)-f(z_0)}{h}$$
 
exists.  
 
exists.  
  
 
=Properties=
 
=Properties=
{{:Derivative is a linear operator}}
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[[Derivative is a linear operator]]<br />
{{:Relationship between q-derivative and derivative}}
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[[Relationship between q-derivative and derivative]]

Latest revision as of 05:10, 26 November 2016

Let $D$ be a subset of complex numbers, $z_0 \in D$, and let $f \colon D \rightarrow \mathbb{C}$ be a function. We say that $f$ is (complex-) differentiable at $z_0$ if the limit $$f'(z_0)=\displaystyle\lim_{h \rightarrow 0} \dfrac{f(z_0+h)-f(z_0)}{h}$$ exists.

Properties

Derivative is a linear operator
Relationship between q-derivative and derivative