Determine a derivada da função y = 3 / 3raiz de x + 3raiz de x / 3

540

\(\frac{d}{dx}\left(\frac{3}{3\sqrt{x}}+\frac{3\sqrt{x}}{3}\right)> derivaçao por partes parte 1> =\frac{d}{dx}\left(\frac{3}{3\sqrt{x}}\right)+\frac{d}{dx}\left(\frac{3\sqrt{x}}{3}\right)> \frac{d}{dx}\left(\frac{3}{3\sqrt{x}}\right)> =1\frac{d}{dx}\left(\frac{1}{\sqrt{x}}\right)> =1\frac{d}{dx}\left(x^{-\frac{1}{2}}\right)> =1\cdot \left(-\frac{1}{2}x^{-\frac{1}{2}-1}\right)> =-1\cdot \frac{1}{2}x^{-\frac{1}{2}-1}> x^{-\frac{1}{2}-1}> -\frac{1}{2}-1> =-\frac{1\cdot \:2}{2}-\frac{1}{2}> =\frac{-1\cdot \:2-1}{2}> =\frac{-3}{2}> =-\frac{3}{2}> =x^{-\frac{3}{2}}> =-1\cdot \frac{1}{2}x^{-\frac{3}{2}}> =1\cdot \frac{1}{2}\cdot \frac{1}{x^{\frac{3}{2}}}> =-1\cdot \frac{1\cdot \:1}{2x^{\frac{3}{2}}}> =-\frac{1}{2x^{\frac{3}{2}}}> Parte 2 \frac{d}{dx}\left(\frac{3\sqrt{x}}{3}\right)> =1\frac{d}{dx}\left(\sqrt{x}\right)> =1\frac{d}{dx}\left(x^{\frac{1}{2}}\right)> =1\cdot \frac{1}{2}x^{\frac{1}{2}-1}> x^{\frac{1}{2}-1}=x^{-\frac{1}{2}}> x^{-\frac{1}{2}}> \frac{1}{2}-1> =-\frac{1\cdot \:2}{2}+\frac{1}{2}> =\frac{-1\cdot \:2+1}{2} =\frac{-1}{2}> =-\frac{1}{2}> =x^{-\frac{1}{2}}> =1\cdot \frac{1}{2}x^{-\frac{1}{2}}> x^{-\frac{1}{2}}=\frac{1}{\sqrt{x}}> =1\cdot \frac{1}{2}\cdot \frac{1}{\sqrt{x}}> =1\cdot \frac{1\cdot \:1}{2\sqrt{x}}> =\frac{1}{2\sqrt{x}}> =-\frac{1}{2x^{\frac{3}{2}}}+\frac{1}{2\sqrt{x}} \)