Question

Use the definition of a derivative to find f’(x).

Answer 1

Answer:

f'(x) = $-\frac{9}{x^2}$

Step-by-step explanation:

i) f(x) = 9 / x

ii) f'(x)  = $\lim_{h\to 0} \frac{f(x+h) - f(x)}{h} \hspace{0.2cm}$

        $= \lim_{h\to 0} \frac{\frac{9}{x+h} - \frac{9}{x} }{h} = \hspace{0.1cm} \lim_{h\to 0} \frac{9x - 9(x+h)}{hx(x+h)} \hspace{0.1cm} = \hspace{0.1cm} \lim_{h\to 0} \frac{-9h}{hx(x+h)} = \lim_{h\to 0} \frac{-h}{x(x+h)} = \frac{-9}{x^2}$