Derivadas Simples II - Soluciones
Solución 1
\[f(x) = \sqrt{x}\]
\[f'(x) = \boxed{\frac{1}{2 \sqrt{x}}}\]
\[f'(x) = \boxed{\frac{1}{2 \sqrt{x}}}\]
Solución 2
\[f(x) = \sqrt[3]{x}\]
\[f'(x) = \boxed{\frac{1}{3 \sqrt[3]{x^2}}}\]
\[f'(x) = \boxed{\frac{1}{3 \sqrt[3]{x^2}}}\]
Solución 3
\[f(x) = \sqrt[4]{x}\]
\[f'(x) = \boxed{\frac{1}{4 \sqrt[4]{x^3}}}\]
\[f'(x) = \boxed{\frac{1}{4 \sqrt[4]{x^3}}}\]
Solución 4
\[f(x) = x^{\frac{1}{2}}\]
\[f'(x) = \boxed{\frac{1}{2}x^{\frac{-1}{2}}}\]
\[f'(x) = \boxed{\frac{1}{2}x^{\frac{-1}{2}}}\]
Solución 5
\[f(x) = x^{\frac{1}{3}}\]
\[f'(x) = \boxed{\frac{1}{3}x^{\frac{-2}{3}}}\]
\[f'(x) = \boxed{\frac{1}{3}x^{\frac{-2}{3}}}\]
Solución 6
\[f(x) = 7\sqrt{x}\]
\[f'(x) = \boxed{\frac{7}{2 \sqrt{x}}}\]
\[f'(x) = \boxed{\frac{7}{2 \sqrt{x}}}\]
Solución 7
\[f(x) = 7x^{\frac{2}{3}}\]
\[f'(x) = \boxed{\frac{14}{3}x^{\frac{-1}{3}}}\]
\[f'(x) = \boxed{\frac{14}{3}x^{\frac{-1}{3}}}\]