Final answer:
The derivative of the function f(x) = 4x⁵ - 6eˣ, denoted as f'(x), is found by applying the power rule to the polynomial term and the constancy of the exponential function's derivative to obtain 20x⁴ - 6eˣ, which is answer choice a).
Step-by-step explanation:
To find the derivative of f(x) = 4x⁵ - 6eˣ, we use the power rule and the derivative of the exponential function.
The power rule states that the derivative of xⁿ is n*x^(n-1).
The derivative of eˣ is eˣ.
So, using the power rule, the derivative of 4x⁵ is 20x⁴, and the derivative of -6eˣ is -6eˣ.If f(x) = 4x⁵ - 6eˣ, to find f'(x), you need to take the derivative of each term separately using the rules of differentiation. The derivative of 4x⁵ is 20x⁴, because according to the power rule, you bring down the exponent and subtract one from that exponent. The derivative of -6eˣ is -6eˣ, because the derivative of eˣ with respect to x is eˣ, and the coefficient -6 remains unchanged.
Thus, the derivative, f'(x), is 20x⁴ - 6eˣ.
Therefore, the correct answer is a) 20x⁴ - 6eˣ.