微分公式(2)
Author: 藍邦偉　老師

微分公式(2)

c為常數，則：\frac{dc}{dx}=0

Pf

設f(x)=c

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

=\lim_{ h\to 0 }\frac{c-c}{h}=0

c為常數，則\frac{d}{dx}\left [c\cdot f(x)  \right ] =c \cdot \frac{df(x)}{dx}

$ \frac{d}{dx}\left [c\cdot f(x)  \right ]=\lim_{ h \to 0 }\frac{cf(x+h)-cf(x)}{h}  $

=\lim_{ h \to 0 }c\cdot \frac{f(x+h)-f(x)}{h}

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

=c \cdot \frac{d}{dx} f(x)

Pf

Step = 0 (slider from 0 to 7, step 1)
S = 0