Question

Qual a derivada da raiz quadrada de x?

Answer 1

$\sqrt{x} \\ \\ x^{ \frac{1}{2} } \\ \\ \frac{1}{2}. x^{ \frac{1}{2}-1 } \\ \\ \frac{1}{2}. x^{ - \frac{1}{2} } \\ \\ \frac{1}{2}. \frac{1}{ \sqrt{x} } \\ \\ \frac{ \sqrt{x} }{2x}$

Answer 2

$f(x) = \sqrt{x} = x^{ \frac{1}{2}$
$f'(x) = \frac{1}{2} x^{ (\frac{1}{2} -1) } = \frac{1}{2} x^{ -\frac{1}{2} } = \frac{1}{2 \sqrt{x} }$