it is impossible for me to find derivative of the function f(x)=x^(2*square root x)

To find derivative of the function, first we'll take
natural logarithms both sides:

ln f(x) = ln x^(2*sqrt
x)

We'll use the property of
logarithms:

ln f(x) = (2*sqrt x)*ln
x

Now, we'll differentiate both sides, with respect to
x:

[ln f(x)]' = [(2*sqrt x)*ln
x]'

We'll apply the product rule to the right
side:

f'(x)/f(x) = 2*ln x/2sqrtx + 2*sqrt
x/x

f'(x)/f(x) = ln x/sqrtx + 2*sqrt
x/x

f'(x)/f(x) = (sqrt x*ln x + 2sqrt
x)/x

f'(x) = f(x)*(sqrt x*ln x + 2sqrt
x)/x

f'(x) = [x^(2sqrt x)]*(sqrt x)*(ln x +
2)/x

The first derivative of the given
function is: f'(x) = [x^(2sqrt x)]*(sqrt x)*(ln x +
2)/x