Question

Utilizando as regras de derivação, faça o cálculo ANEXO

Answer 1

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Solução!


Para resolver esse exercício basta aplicar a formula da derivada do quociente.


$\boxed{ \left (\dfrac{u}{v} \right )'=\left \dfrac{v.u'-u.v'}{(v)^{2} } \right }$


$f(x)= \dfrac{4cos(x)}{3x} \\\\\\\\\ u=cos(x)~~~~~u'=-sen(x)\\\\\\ v=x~~~~~v'=1\\\\\\\\ Substituindo!\\\\\\\\ \left \dfrac{v.u'-u.v'}{(v)^{2} } \right \\\\\\\\\ \left (\dfrac{4cos(x)}{3x} \right )= \dfrac{4}{3} \left( \dfrac{x.(-sen(x))-cos(x).(1)}{(x)^{2} } \right )\\\\\\\\ \left (\dfrac{4cos(x)}{3x} \right )= \left(- \dfrac{4}{3} \dfrac{x.sen(x)-cos(x).(1)}{x^{2} } \right )\\\\\\\\ \left (\dfrac{4cos(x)}{3x} \right )= \left( \dfrac{-4x.sen(x)+cos(x).}{3x^{2} } \right )$


$\boxed{Resposta: \left( \dfrac{-4x.sen(x)+cos(x).}{3x^{2} } \right )~~\boxed{Alternativa~~A}}$


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