Differentiatef(x)=(x+1)12𝑓(𝑥)=(𝑥+1)12.Select one:A.12(x+1)−1212(𝑥+1)−12B.−12(x+1)−12−12(𝑥+1)−12C.12(x+1)1212(𝑥+1)12D.12(x+1)−32

The function given is f(x) = (x+1)^(1/2).

To differentiate this function, we will use the power rule for differentiation, which states that the derivative of x^n is n*x^(n-1).

Step 1: Identify the base (x+1) and the exponent (1/2).

Step 2: Apply the power rule. Multiply the entire function by the exponent, then subtract 1 from the exponent.

This gives us: (1/2)*(x+1)^(1/2 - 1)

Step 3: Simplify the exponent.

This gives us: (1/2)*(x+1)^(-1/2)

Step 4: Rewrite the expression to make it more readable.

This gives us: (1/2)*(1/√(x+1))

So, the derivative of f(x) = (x+1)^(1/2) is f'(x) = (1/2)*(1/√(x+1)).

This corresponds to none of the options given in the question. There might be a mistake in the options.