Final answer:
To find the derivative of the function f(x) = √(5x + 2), apply the power rule for derivatives. The derivative is (5/2)(5x + 2)^(-1/2).
Step-by-step explanation:
To find the derivative of the function f(x) = √(5x + 2), we can use the power rule for derivatives. The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n * x^(n-1).
In this case, n = 1/2 because the exponent is √(5x + 2) is 1/2. So, we can apply the power rule to find the derivative:
f'(x) = (1/2)(5x + 2)^(1/2 - 1) * (d/dx)(5x + 2)
f'(x) = (1/2)(5x + 2)^(-1/2) * 5
f'(x) = (5/2)(5x + 2)^(-1/2)