Question

Qual é a derivada de x^x?

Answer 1

$y=x^x\\\\ln(y)= ln(x^x)\\\\ln(y)=x*ln(x)\\\\\ [ln(y)]' = [x*ln(x)]'\\\\\text{derivando os dois lados em relacao a x}\\\\ \frac{1}{y}*y' = [x'*ln(x)+x*ln(x)']\\\\ \frac{1}{y}*y' = [1*ln(x)+x* \frac{1}{x} ]\\\\ \frac{1}{y}*y' = ln(x)+1\\\\y' = (ln(x)+1)*y\\\\\text{como } y= x^x\\\\\boxed{\boxed{y'=(ln(x)+1)*x^{x}}}$