MATEMATIKA INDONESIA: Turunan 2

contoh 3
$f(x)=\frac{1}{x}$ maka $f(x+h)=\frac{1}{x+h}$
sehingga :
$f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\rightarrow 0}\frac{\frac{1}{x+h}-\frac{1}{x}}{h}=\lim_{h\rightarrow 0} \frac{\left ( \frac{x-(x+h)}{x(x+h) \right )}{}}{h}$

$=\lim_{h\rightarrow 0} \frac{\left ( \frac{-h}{x(x+h) \right )}{}}{h} = \lim_{h\rightarrow 0}\frac{-1}{x(x+h)}=\frac{-1}{x(x+0)}=-\frac{1}{x^{2}}$

contoh 3
$f(x)=\sqrt{x}$ maka $f(x+h)=\sqrt{x+h}$

$f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\rightarrow 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}$

$= \lim_{h\rightarrow 0}\left ( \frac{\sqrt{x+h}-\sqrt{x}}{h} \right ). \left ( \frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}} \right )$

$= \lim_{h\rightarrow 0}\frac{x+h-x}{h\left ( \sqrt{x+h}+\sqrt{x} \right )}= \lim_{h\rightarrow 0}\frac{h}{h\left ( \sqrt{x+h}+\sqrt{x} \right )}$
$= \lim_{h\rightarrow 0}\frac{1}{\sqrt{x+h}+\sqrt{x}}=\frac{1}{\sqrt{x+0}+\sqrt{x}}=\frac{1}{2\sqrt{x}}$

materi sebelumnya
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MATEMATIKA INDONESIA

Rabu, 04 Agustus 2010

Turunan 2

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