Question

Calcular a derivada da função:

y= sen( x⁴ ) / 6x+8

Answer 1

Calcular a derivada da função

     $y=\dfrac{\mathrm{sen}(x^4)}{6x+8}$


Aqui temos que aplicar a regra da derivada do quociente:

     $\dfrac{dy}{dx}=\dfrac{d}{dx}\!\left(\dfrac{\mathrm{sen}(x^4)}{6x+8}\right)\\\\\\ \dfrac{dy}{dx}=\dfrac{\frac{d}{dx}\big[\mathrm{sen}(x^4)\big]\cdot (6x+8)-\mathrm{sen}(x^4)\cdot \frac{d}{dx}(6x+8)}{(6x+8)^2}\\\\\\ \dfrac{dy}{dx}=\dfrac{\big[\cos(x^4)\cdot \frac{d}{dx}(x^4)\big]\cdot (6x+8)-\mathrm{sen}(x^4)\cdot \frac{d}{dx}(6x+8)}{(6x+8)^2}\\\\\\ \dfrac{dy}{dx}=\dfrac{\cos(x^4)\cdot 4x^3\cdot (6x+8)-\mathrm{sen}(x^4)\cdot 6}{(6x+8)^2}$

     $\dfrac{dy}{dx}=\dfrac{4x^3(6x+8)\cos(x^4)-6\,\mathrm{sen}(x^4)}{(6x+8)^2}\quad\longleftarrow\quad\mathsf{resposta.}$


Dúvidas? Comente.


Bons estudos! :-)