Turunan Fungsi Aturan Selisih


Sifat 1.

Jika f dan g fungsi-fungsi yang terdiferensial maka (f – g)(x) = f(x) – g(x) yakni Dx[f(x) – g(x)] = Dx[f(x)] – Dx[g(x)]

Bukti.

Andaikan F(x) = f(x) – g(x)

F'(x) = \lim \sb{h \to 0} \dfrac{\left [ f(x+h) - g(x+h)\right ]-\left [ f(x) - g(x)\right ]}{h}

= \lim \sb{h \to 0} \dfrac{\left [ f(x+h) - g(x+h) - f(x) + g(x)\right ]}{h}

= \lim _{h \to 0}\left (\dfrac{f(x+h)-f(x)}{h} - \dfrac{g(x+h)-g(x)}{h} \right )

= \lim \sb{h \to 0} \dfrac{f(x+h)-f(x)}{h} - \lim \sb{h \to 0} \dfrac{g(x+h)-g(x)}{h}

= f'(x) – g'(x) \blacksquare

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