Question

Por favor preciso de ajuda, está no anexo.
(D)


(C)


(B)


(A)


(E)

Answer 1

$y=\mathrm{\ell n}\left(2x^{3} \right )\cdot \mathrm{sen\,}x\\ \\ \\ y'=\left[\,\mathrm{\ell n}\left(2x^{3} \right )\, \right ]'\cdot \mathrm{sen\,}x+\mathrm{\ell n}\left(2x^{3} \right )\cdot \left(\mathrm{sen\,}x \right )'\\ \\ y'=\dfrac{1}{2x^{3}}\cdot \left(2x^{3} \right )'\cdot \mathrm{sen\,}x+\mathrm{\ell n}\left(2x^{3} \right )\cdot \cos x\\ \\ y'=\dfrac{1}{2x^{3}}\cdot \left(3\cdot 2x^{3-1} \right )\cdot \mathrm{sen\,}x+\mathrm{\ell n}\left(2x^{3} \right )\cdot \cos x\\ \\ y'=\dfrac{1}{2x^{3}}\cdot \left(6x^{2} \right )\cdot \mathrm{sen\,}x+\mathrm{\ell n}\left(2x^{3} \right )\cdot \cos x\\ \\ y'=\dfrac{6x^{2}\cdot \mathrm{sen\,}x}{2x^{3}}+\mathrm{\ell n}\left(2x^{3} \right )\cdot \cos x\\ \\ y'=\dfrac{\diagup\!\!\!\!\!\! 2x^{2}\cdot \left(3\mathrm{\,sen\,}x \right )}{\diagup\!\!\!\!\!\! 2x^{2}\cdot x}+\mathrm{\ell n}\left(2x^{3} \right )\cdot \cos x\\ \\ \boxed{y'=\dfrac{3\mathrm{\,sen\,}x}{x}+\mathrm{\ell n}\left(2x^{3} \right )\cdot \cos x}$


Resposta: alternativa $\text{(C) }y'=\mathrm{\ell n}\left(2x^{3} \right )\cdot \cos x+\dfrac{3\mathrm{\,sen\,}x}{x}$.