# Find f'(x) if f(x)=sqrt(9-x) and state its domains of f'(x) =lim_(h -> 0) (f(x+h)-f(x))/(h) =lim_{h -> 0) (sqrt(9-(x+h))-sqrt(9-x))/(h) ((sqrt(9-(x+h))+sqrt(9-x))/(sqrt(9-(x+h))+sqrt(9-x)))

Find f'(x) if $f\left(x\right)=\sqrt{9-x}$ and state its domains of f'(x)
$=\underset{h\to 0}{lim}\frac{f\left(x+h\right)-f\left(x\right)}{h}\phantom{\rule{0ex}{0ex}}=\underset{h\to 0}{lim}\frac{\sqrt{9-\left(x+h\right)}-\sqrt{9-x}}{h}\left(\frac{\sqrt{9-\left(x+h\right)}+\sqrt{9-x}}{\sqrt{9-\left(x+h\right)}+\sqrt{9-x}}\right)$
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kitskjeja
Given
$⇒x\in \left(-\mathrm{\infty },9\right)$
$\therefore$ demain of f'(x) is $\left(-\mathrm{\infty },9\right)$