Final answer:
The derivative of 2√x is found by rewriting it as 2x^{1/2} and applying the power rule to obtain 1x^{-1/2}, which simplifies to 1/√x. The correct answer is A) 1/√x.
Step-by-step explanation:
To find the derivative of 2√x, we can rewrite the function in a form that makes it easier to differentiate. Recall that the square root of a variable can be expressed as a fractional power, so √x = x^ {1/2}. Thus, the function 2√x can be rewritten as 2x^{1/2}.
To differentiate this function, we use the power rule. The power rule states that if you have a function of the form x^n, its derivative is nx^{n-1}. Applying this to our function:
Multiply the coefficient (2) by the exponent (1/2).
Subtract 1 from the exponent to get the new exponent (1/2 - 1 = -1/2).
The result is (2 × 1/2)x^{-1/2} = 1x^ {-1/2}, which simplifies to 1/√x. Therefore, the correct answer is A) 1/√x.