Question

Qual é a 1ª e a 2ª derivada das seguintes funções? (Me ajudem por favor)

a) y= x - 3x^1/3

b) y= 5x^2/3 - x^5/3

Answer 1

Bom dia Rafaela!


Solução!


$y=x-3x^{ \frac{1}{3} }\\\\\ y'=1- \frac{1}{3}.3x^{ \frac{1}{3}-1 }\\\\\\ y'=1-x^{ -\frac{2}{3} }\\\\\ y'=1- \frac{1}{ x^{ \frac{2}{3} } }\\\\\\ y'=1- \frac{1}{ \sqrt[3]{ x^{2} } }\\\\\\\ \boxed{Resposta: y'=1- \frac{1}{ \sqrt[3]{ x^{2} } }}$



$y=5x^{ \frac{2}{3} } -x^{ \frac{5}{3} }\\\\\\\ y= \frac{2}{3}. 5x^{ \frac{2}{3}-1 } - \frac{5}{3} .x^{ \frac{5}{3}-1 }$


$y= \frac{2}{3}. 5x^{ \frac{2}{3}-1 } - \frac{5}{3} .x^{ \frac{5}{3}-1 }\\\\\\\ y'= \frac{10 x^{ -\frac{1}{3} } }{3 }- \frac{5 x^{ \frac{2}{3} } }{3} \\\\\\\ y'= \frac{1}{3.10 x^{ \frac{1}{3} } } -\frac{5 x^{ \frac{2}{3} } }{3} \\\\\\\ y'= \frac{1}{3. \sqrt[3]{10x} } }- \frac{5 \sqrt[3]{ x^{2} } }{3} \\\\\\\\\\\ \boxed{Resposta:y'= \frac{1}{3. \sqrt[3]{10x} } - \frac{5 \sqrt[3]{ x^{2} } }{3}}$


Bom dia!
Bons estudos!