Question

Resolva. F'(x) pela definiçao
f(x)= 1/x

X=1

Answer 1

Derivada no ponto

$\boxed{f'(a)=\lim_{x \to \ a}\frac{f(x)-f(a)}{x-a}}$

$f'(1)=\lim_{x \to \ 1}\frac{\frac{1}{x} -\frac{1}{1}}{x-1}$

$f'(1)=\lim_{x \to \ 1}\frac{\frac{1-x}{x}}{x-1}$

$f'(1)=\lim_{x \to \ 1}\frac{1-x}{x}.\frac{1}{x-1}$

$f'(1)=\lim_{x \to \ 1}-\frac{x-1}{x}.\frac{1}{x-1}$

$\boxed{f'(1)=\lim_{x \to \ 1}-\frac{1}{x}}$

$\boxed{f'(1)=-1}$