How to differentiate x^2 - 8√(2x) +17

I was stuck to differentiate 8√(2x)

Can anyone show me steps by steps ?

y = x² - 8√2x + 17
y = x² - 8[√2)(√x)] + 17
y = x² - 8√2(x)^½ + 17

dy/dx = 2x - (8√2)½(x)ˉ½ + 0
dy/dx = 2x - 8√2(1 / 2√x)
dy/dx = 2x - (4√2 / √x)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Well first split √(2*x) into √2*√x.
Then write it in the form 8 * 2^(1/2) * x^(1/2).
Then just treat 8 * 2^(1/2) as a regular coefficient and differentiate x^(1/2) the normal way by chucking the power out front and then taking 1, eg

d/dx(8√(2x)) = 8 * 2^(1/2) * 1/2 * x^(-1/2) = 4√2/√x

That makes the whole equation:
d/dx(x^2 - 8√(2x) +17) = 2x + 4√2/√x

As given question has to read as :-
f (x) = x² - (8√2) √x + 17
f (x) = x² - (8√2) x^(1/2) + 17
f ` (x) = 2x - 4√2 x^(-1/2)
f ` (x) = 2x - 4√2/√x