How to differentiate the square root function f(x) = √(1 - x). 

Differentiation or derivative are important concepts that have many applications. In this section, we will learn how to differentiate a square root function.

Answer: The derivative of the square root function f(x) is -1 / [2√(1 - x)].

Let's understand the solution in detail.

Explanation:

Given function: f(x) = √(1 - x) = (1 - x)^1/2

First, we use the property d(xⁿ) / dx = nx^{n - 1}, and then the chain rule.

Hence, d[√(1 - x)] / dx = 1/2 × (1 - x)^-1/2 . [1 - d(x)/dx]

Therefore, (√(1 - x) / dx = -1/2 × [1/√(1 - x)]

Hence, the derivative of the square root function f(x) = √(1 - x) is -1 / [2√(1 - x)].