Aplique ln aos dois membros:\(ln(y)=ln\left(\frac{1}{\frac{\sqrt[3]{3x+2}}{\sqrt[3]{5^{x}}}}\right)\)
\(ln(y)=ln(1)-ln\left(\frac{\sqrt[3]{3x+2}}{\sqrt[3]{5^{x}}}\right)\)
\(ln(y)=-ln\left(\frac{(3x+2)^{\frac{1}{3}}}{5^{\frac{x}{3}}}\right)\)
\(ln(y)=-\left(ln(3x+2)^{\frac{1}{3}}-ln(5^{\frac{x}{3}})\right)\)
\(ln(y)=-ln(3x+2)^{\frac{1}{3}}+ln(5^{\frac{x}{3}})\)
\(ln(y)=-\frac{1}{3}*ln(3x+2)+\frac{x}{3}*ln(5)\)
\(ln(y)=-\frac{1}{3}*ln(3x+2)+\frac{x}{3}*ln(5)\)
derive:
\(\frac{y'}{y}=-\frac{1}{3}*\frac{3}{(3x+2)}+\frac{ln(5)}{3}\)
\(\frac{y'}{y}=-\frac{3}{9x+6}+\frac{ln(5)}{3}\)
\(y'=y*(-\frac{3}{9x+6}+\frac{ln(5)}{3})\)
\(y'=(\frac{1}{\frac{\sqrt[3]{3x+2}}{\sqrt[3]{5^{x}}}})*(-\frac{3}{9x+6}+\frac{ln(5)}{3})\)
se houver dúvidas é só dizer
, tente fazer a outra questão.