Final answer:
To find the derivative of the function f(x) = x⁵ * (5)ˣ, use the product rule. The derivative is 5ˣ * (5x⁴ + x⁵ * ln(5)).
Step-by-step explanation:
To find the derivative of the function f(x) = x⁵ * (5)ˣ, we need to use the product rule. The product rule states that the derivative of the product of two functions is equal to the derivative of the first function multiplied by the second function, plus the first function multiplied by the derivative of the second function.
Applying the product rule to f(x) = x⁵ * (5)ˣ:
f'(x) = (5)ˣ * 5x⁴ + x⁵ * ln(5) * (5)ˣ
Simplifying further:
f'(x) = 5ˣ * (5x⁴ + x⁵ * ln(5))