Question

qual e a derivada de raiz de x + raiz cubica de x

Answer 1

$f(x) = \sqrt{x+ \sqrt[3]{x} } \\\\f(x) = (x+ x^{ \frac{1}{3} })^{ \frac{1}{2} }\\\\ f'(x) = \frac{1}{2}*(x+x^{ \frac{1}{3} })^{ \frac{1}{2} -1} *(x+x^{ \frac{1}{3} })'\\\\ \boxed{f'(x) = \frac{1}{2 \sqrt{x+ \sqrt[3]{x} } }*(x+x^{ \frac{1}{3} })' }$

derivando oque esta dentro do parenteses
$(x+x^{ \frac{1}{3} })'\\\\= 1+ \frac{1}{3}*x^{ \frac{1}{3}-1 } \\\\=1+ \frac{1}{3}*x^{- \frac{2}{3} } \\\\=1+ \frac{1}{3 \sqrt[3]{x^2} }$

resposta
$\boxed{f'(x) = \frac{1}{2 \sqrt{x+ \sqrt[3]{x} } } * (1+\frac{1}{ \sqrt[3]{x^2} } )}$