Question

Please derivate this
`(2x√(x) )/(3)`

Answer 1

`f'(x)=√(x)`

Explanation:

We begin with the given function

`f(x)=(2x√(x) )/(3)`

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

`f(x)=(2x√(x) )/(3)\\\\f(x)=(2)/(3) (x)(x^{(1)/(2) } )\\\\f(x)=(2)/(3) x^{(3)/(2) }`

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

`f'(x)=(3)/(2) *(2)/(3) x^{(1)/(2) } \\\\f'(x)=x^{(1)/(2) } \\\\f'(x)=√(x)`