$=\underset{h\to 0}{lim}\frac{f(x+h)-f(x)}{h}\phantom{\rule{0ex}{0ex}}=\underset{h\to 0}{lim}\frac{\sqrt{9-(x+h)}-\sqrt{9-x}}{h}(\frac{\sqrt{9-(x+h)}+\sqrt{9-x}}{\sqrt{9-(x+h)}+\sqrt{9-x}})$

Ciara Rose
2022-07-16
Answered

Find f'(x) if $f(x)=\sqrt{9-x}$ and state its domains of f'(x)

$=\underset{h\to 0}{lim}\frac{f(x+h)-f(x)}{h}\phantom{\rule{0ex}{0ex}}=\underset{h\to 0}{lim}\frac{\sqrt{9-(x+h)}-\sqrt{9-x}}{h}(\frac{\sqrt{9-(x+h)}+\sqrt{9-x}}{\sqrt{9-(x+h)}+\sqrt{9-x}})$

$=\underset{h\to 0}{lim}\frac{f(x+h)-f(x)}{h}\phantom{\rule{0ex}{0ex}}=\underset{h\to 0}{lim}\frac{\sqrt{9-(x+h)}-\sqrt{9-x}}{h}(\frac{\sqrt{9-(x+h)}+\sqrt{9-x}}{\sqrt{9-(x+h)}+\sqrt{9-x}})$

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