Question

Please derivate this \sqrt{x} }{3}" alt="\frac{2x\sqrt{x} }{3}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$f'(x)=\sqrt{x}$

Step-by-step explanation:

We begin with the given function

$f(x)=\frac{2x\sqrt{x} }{3}$

Before we differentiate this function, let us do some manipulations to make this much easier

$f(x)=\frac{2x\sqrt{x} }{3}\\\\f(x)=\frac{2}{3} (x)(x^{\frac{1}{2} } )\\\\f(x)=\frac{2}{3} x^{\frac{3}{2} }$

Now we can use the power rule to differentiate this and then simplify

$f'(x)=\frac{3}{2} *\frac{2}{3} x^{\frac{1}{2} } \\\\f'(x)=x^{\frac{1}{2} } \\\\f'(x)=\sqrt{x}$