To find the derivative of a square root function, we can use the power rule of differentiation and the chain rule method. The derivative of the square root of x is given by d(√x)/dx = (1/2) x-1/2 or 1/(2√x) . We can also rewrite the square root as an exponent, where the term below the square root sign is written as the base, and it is raised to the exponent of 1/2. For example, if we have 2√x, we can rewrite it as 2x^(1/2), and then apply the power rule to get the derivative of x^(1/2), which is (1/2)x^(-1/2) .

In summary, the derivative of a square root function is given by the derivative of the radicand, divided by double the original square root. Symbolically, this can be shown as: d(√x)/dx = d(x^(1/2))/dx = (1/2)x^(-1/2) = 1/(2√x) .