Find the derivative of the power function: y = sqrt (2x).

Find the derivative of the power function y = √ (2 * x).

In order to find the derivative of a function, we use the derivative formulas:

(x + y) ‘= x’ + y ‘;
sin ‘x = cos x;
(x / y) ‘= (x’ * y – y ‘* x) / y ^ 2;
(x ^ n) ‘= n * x ^ (n – 1);
x ‘= 1;
C ‘= 0;
cos’ x = -sin x.
Then we get:

y ‘= (√ (2 * x))’ = √2 * (√x) ‘= √2 * (x ^ (1/2))’ = √2 * 1/2 * x ^ (1/2 – 1) = √2 / 2 * x ^ (0.5 – 1) = √2 / 2 * x ^ (- 0.5) = √2 / (2 * √x));

As a result, we got, y ‘= √2 / (2 * √x)).