Question

A primeira derivadada função F(x)=3(5x-4)^3 É?

Answer 1

Calcular a derivada da função

     $\mathsf{f(x)=3(5x-4)^3}$

Aqui devemos aplicar a Regra da Cadeia:

     $\mathsf{\dfrac{d}{dx}\big[f(x)\big]=\dfrac{d}{dx}\big[3(5x-4)^3\big]}\\\\\\ \mathsf{\dfrac{d}{dx}\big[f(x)\big]=3\cdot \dfrac{d}{dx}\big[(5x-4)^3\big]}\\\\\\ \mathsf{\dfrac{d}{dx}\big[f(x)\big]=3\cdot 3(5x-4)^{3-1}\cdot \dfrac{d}{dx}(5x-4)}\\\\\\ \mathsf{\dfrac{d}{dx}\big[f(x)\big]=3\cdot 3(5x-4)^2\cdot 5}$

     $\mathsf{\dfrac{d}{dx}\big[f(x)\big]=45(5x-4)^2\quad\longleftarrow\quad esta~\acute{e}~a~resposta.}$


Dúvidas? Comente.


Bons estudos! :-)