Answer:
[tex]f'(x)=\sqrt{x}[/tex]
Step-by-step explanation:
We begin with the given function
[tex]f(x)=\frac{2x\sqrt{x} }{3}[/tex]
Before we differentiate this function, let us do some manipulations to make this much easier
[tex]f(x)=\frac{2x\sqrt{x} }{3}\\\\f(x)=\frac{2}{3} (x)(x^{\frac{1}{2} } )\\\\f(x)=\frac{2}{3} x^{\frac{3}{2} }[/tex]
Now we can use the power rule to differentiate this and then simplify
[tex]f'(x)=\frac{3}{2} *\frac{2}{3} x^{\frac{1}{2} } \\\\f'(x)=x^{\frac{1}{2} } \\\\f'(x)=\sqrt{x}[/tex]
