Final answer:
The derivative of √(xy) is x/(2√(xy)). Option (B) is correct.
Step-by-step explanation:
The derivative is defined as the method that shows the simultaneous rate of change. That means it is used to represent the amount by which the given function is changing at a certain point.
A derivative is described as either the rate of change of a function, or the slope of the tangent line at a particular point on a function. What is a derivative in simple terms? A derivative tells us the rate of change with respect to a certain variable.
The derivative of √(xy) can be found using the chain rule. Let's start by expressing √(xy) as (xy)1/2. Now, we can differentiate it as follows:
d/dx(√(xy)) = (1/2)(xy)-1/2(d/dx(xy)) = (1/2)(xy)-1/2(y+xdy/dx) = (1/2)(xy)-1/2(y+xy') = y/(2√(xy)) + x/(2√(xy))y'
Therefore, the correct answer is option B: x/(2√(xy)).