Derivative of a square root?

Question

How do you find the derivative of the squareroot of x?

Answer 1

sqrt(x) = x^(0.5)

derivative of x^n is just nx^(n-1)

here n =0.5
hence the derivative of sqrt(x) = 0.5x^(0.5-1)
0.5x^(-0.5) or

=1/(2sqrt(x))

Answer 2

The derivative of a function f(x) = x^r is:

f'(x) = (r-1)x^(r-1)

So for square root, r = 1/2. The derivative would be:

(1/2) * x^(-1/2)

Answer 3

Easy. Recall that sqrt(x) = x^(1/2).
Now use the power rule to do the derivitive to get
d(sqrt(x))/dx = (1/[2sqrt(x)])