[tex]\displaystyle \\
x \sqrt{x} = x^1 \times x^{ \frac{1}{2} } = x^{1+ \frac{1}{2}}=x^{\frac{3}{2}} \\ \\
\left(x^{\frac{3}{2}} \right)' = \frac{3}{2} x^{\frac{3}{2}-1}=\frac{3}{2} x^{\frac{1}{2}}=\frac{3}{2} \sqrt{x} = \boxed{\frac{3 \sqrt{x} }{2}}
[/tex]
