Key to "How do you use the limit definition of..."

Max Williams

Answered question

2022-04-12

How do you use the limit definition of the derivative to find the derivative of

f (x) = \frac{2}{x}

blogspainmarax6qi

Beginner2022-04-13Added 12 answers

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

= lim_{h \to 0} \frac{\frac{2}{x + h} - \frac{2}{x}}{h} = lim_{h \to 0} \frac{\frac{2 x - 2 (x + h)}{x (x + h)}}{h}

= lim_{h \to 0} \frac{1}{h} \frac{- 2 h}{x (x + h)} = lim_{h \to 0} \frac{- 2}{x (x + h)} = - \frac{2}{x^{2}}

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

zvonkurm7h

Beginner2022-04-14Added 8 answers

lim_{h \to 0} [\frac{f (x + h) - f (x)}{h}]

= lim_{h \to 0} (\frac{\frac{2}{x + h} - \frac{2}{x}}{h})

lim_{h \to 0} (\frac{\frac{2}{x + h} - \frac{2}{x}}{h}) = - \frac{2}{x^{2}}

= - \frac{2}{x^{2}}

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