Final answer:
The derivative of the constant function f(x) = 2⁵⁰ is 0 because the rate of change of a constant value with respect to a variable is always 0. The correct answer is d) 2⁴9 * ln(2).
Step-by-step explanation:
The question involves differentiating a constant function. The function given is f(x) = 2⁵⁰, which is a constant because it does not have any variable part that depends on x.
When you differentiate a constant function, the derivative is always 0, regardless of the value of the constant. This is a fundamental rule in calculus.
To differentiate the function f(x) = 2^50, we need to use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = x^n, where n is a constant, then the derivative of f(x) is given by f'(x) = n*x^(n-1).
Applying this rule to our function, we have f'(x) = 50*2^(50-1), which simplifies to f'(x) = 50*2^49. So, the correct option is d) 2^49 * ln(2).