Question

Calcule a derivada da função f(x) = x^x​

Answer 1

$\large\boxed{\begin{array}{l}\rm f(x)=x^x\longrightarrow f(x)=e^{x\ell nx}\\\rm f'(x)= e^{x\ell nx}\cdot\bigg(\ell nx+\backslash\!\!\!x\cdot\dfrac{1}{\backslash\!\!\!x}\bigg)\\\\\rm f'(x)=e^{x\ell nx}(\ell nx+1)\\\huge\boxed{\boxed{\boxed{\boxed{\rm f'(x)=x^x\cdot(\ell nx+1)}}}}\end{array}}$