Question

derivada de:
$\sqrt{ {e}^{x} }$
​

Answer 1

Respuesta:

Explicación paso a paso:

$f(x)=\sqrt{e^{x}}\\\\f'(x)=\frac{d}{dx}(\sqrt{e^{x}})=\frac{d}{dx}(e^{x})^{1/2}\\\\f'(x)=\frac{1}{2}(e^{x})^{1/2-1}*(e^{x})\\\\f'(x)=\frac{1}{2}(e^{x})^{-1/2}*e^{x}\\\\f'(x)=\frac{e^{x}}{2(e^{x})^{1/2}}\\\\f'(x)=\frac{e^{x}}{2\sqrt{e^{x}}}=\frac{1}{2}*(e^{x})*(e^{x})^{-1/2}=\frac{1}{2}*(e^{x})*(e^{-x/2})=\\\\=\frac{e^{x/2}}{2}$