Question

find the derivatives of y = sqrt x-4 by first principle

Answer 1

\[(1/2)\sqrt{x-4}\]

Answer 2

\[\left( \sqrt{x-4} \right)\prime\]

This is in the form \[a\left( f(x) \right)^{b}\]
Where the derivative is \[a*b*(f(x))^{b-1}*(f(x))\prime\]

In our case we have,
a = 1
f(x) = x-4
b = 1/2

The derivative of our function is = \[1*(1/2)*(x-4)^{(-1/2)}*1\]