Final answer:
To find the derivative of the function f(x) = (6x⁴ - 5x)⁵, we can use the chain rule. The derivative of f(x) with respect to x is equal to the derivative of g(x)⁵ with respect to g(x), multiplied by the derivative of g(x) with respect to x.
Step-by-step explanation:
To find the derivative of the function f(x) = (6x⁴ - 5x)⁵, we can use the chain rule. Let's denote g(x) = 6x⁴ - 5x. Then f(x) = g(x)⁵. The chain rule states that the derivative of f(x) with respect to x is equal to the derivative of g(x)⁵ with respect to g(x), multiplied by the derivative of g(x) with respect to x.
First, let's find the derivative of g(x). Using the power rule, we differentiate each term: g'(x) = (4 * 6)x³ - 5 = 24x³ - 5.
Next, we differentiate g(x)⁵ with respect to g(x): (g(x)⁵)' = 5g(x)⁴.
Finally, we multiply these two derivatives: f'(x) = 5g(x)⁴ * (24x³ - 5).