Question

dada a função f(x) = ×₊ 1 / tg(x). calcule a derivada correspondente

Answer 1

Resposta:

$\sf f(x)=\dfrac{x+1}{tg\,x}$

Regra do quociente:

$\boxed{\sf\bigg(\dfrac{f(x)}{g(x)}\bigg)'=\dfrac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}}$

$\sf f(x)=\dfrac{(x+1)'(tg\,x)-(x+1)(tg\,x)'}{(tg\,x)^2}$

$\sf f(x)=\dfrac{1(tg\,x)-(x+1)(sec^2\,x)}{tg^2\,x}$

$\red{\sf f(x)=\dfrac{tg\,x-(x+1)(sec^2\,x)}{tg^2\,x}}$