Question

calcule a g`(x) sendo g dada po g(x)= raiz quarta de x

Answer 1

$g\left(x \right )=\sqrt[4]{x}\\ \\ g\left(x \right )=x^{\,^{1}\!\!\!\diagup\!\!_{4}}\\ \\ \\ g'\left(x \right )=\dfrac{1}{4}\cdot x^{\,^{1}\!\!\!\diagup\!\!_{4}-1}\\ \\ g'\left(x \right )=\dfrac{1}{4}\cdot x^{\,^{\left(1-4 \right )}\!\!\!\diagup\!\!_{4}}\\ \\ g'\left(x \right )=\dfrac{1}{4}\cdot x^{\,^{-3}\!\!\!\diagup\!\!_{4}}\\ \\ g'\left(x \right )=\dfrac{1}{4x^{\,^{3}\!\!\!\diagup\!\!_{4}}}\\ \\ \boxed{g'\left(x \right )=\dfrac{1}{4\sqrt[4]{x^{3}}}}$