Final answer:
The derivative of the function f(x) = 5x⁷ is 35x⁶.
Step-by-step explanation:
To find the derivative of the function f(x) = 5x⁷, we can use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = ax^n, where a and n are constants, then the derivative is given by f'(x) = anx^(n-1).
Applying the power rule to the function f(x) = 5x⁷, we have f'(x) = 7(5)x^(7-1) = 35x⁶. Therefore, the derivative of the function f(x) = 5x⁷ is 35x⁶.