Resposta:
[tex]\sf y(x)=x^{-\frac{3}{2}}+x^{\frac{4}{3}}[/tex]
[tex]\sf y'(x)=\frac{d}{dx}(x^{-\frac{3}{2}}+x^{\frac{4}{3}})[/tex]
[tex]\sf y'(x)=\frac{d}{dx}x^{-\frac{3}{2}}+\frac{d}{dx}x^{\frac{4}{3}}[/tex]
[tex]\sf y'(x)=-\frac{3}{2}\cdot x^{-\frac{3}{2}-1}+\frac{4}{3}\cdot x^{\frac{4}{3}-1}[/tex]
[tex]\sf y'(x)=-\frac{3}{2}\cdot x^{-\frac{5}{2}}+\frac{4}{3}\cdot x^{\frac{1}{3}}[/tex]
[tex]\sf y'(x)=-\frac{3}{2}\cdot \frac{1}{x^{\frac{5}{2}}}+\frac{4}{3}\cdot x^{\frac{1}{3}}[/tex]
[tex]\red{\sf y'(x)=-\frac{3}{2x^{\frac{5}{2}}}+\frac{4}{3} x^{\frac{1}{3}}}[/tex]
Regras de derivação usadas:
- [tex]\sf\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)[/tex]
- [tex]\sf\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]
