Turunan Fungsi Aljabar - 1 ~ "BLOGNYA PAK MEMED"

Turunan (Diferensial)

$\large \frac{dy}{dx}=f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$
Dengan menggunakan definisi di-atas, selesaikan soal-soal berikut !
Soal 1
$\large f(x)=x^{2}$
Tentukan f'(x) =
Penyelesaian
$\large \frac{dy}{dx}=f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$
$\large f'(x)=\lim_{h\rightarrow 0}\frac{(x+h^{2})-x}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{x^{2}+2xh+h^{2}-x^{2}}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{2xh+h^{2}}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{h(2x+h)}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\2x+h$
$\large \Leftrightarrow \2x+0=2x$
Soal 2
$\large f(x)=6x^{2}$
Tentukan f'(x) =
$\large \frac{dy}{dx}=f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{6(x+h)^{2}-(6x^{2})}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{6(x^{2}+2xh+h^{2})-6x^{2}}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{6x^{2}+12xh+h^{2}-6x^{2}}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{12xh+h^{2}}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\frac{h(12x+h)}{h}$
$\large \Leftrightarrow \lim_{h\rightarrow 0}\12x+h$
$\large \Leftrightarrow \12x+0=12x$

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Minggu, 07 Oktober 2018

Turunan Fungsi Aljabar - 1

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