Final answer:
To find the derivative of the given function, we can use the power rule and simplify the expression.
Step-by-step explanation:
To find the derivative of the function f(x) = 2^(x + 1) - 2^(x - 1), we can use the power rule. The power rule states that if we have a function of the form g(x) = a^x, the derivative is given by g'(x) = ln(a) * a^x. Applying this rule, we get:
f'(x) = ln(2) * 2^(x + 1) - ln(2) * 2^(x - 1)
Simplifying further, we have:
f'(x) = 2^x * (2 * ln(2) - 1/2 * ln(2))