How do you find the derivative of the function f(x) = 5x^9 at x = 2?

To find the derivative of the function f(x) = 5x^9 at x = 2, you’ll want to follow these steps:

1. First, apply the power rule of differentiation. The power rule states that if you have a term of the form ax^n, the derivative is given by n * a * x^(n-1).

2. In our case, f(x) = 5x^9, where a = 5 and n = 9. Therefore, the derivative f'(x) is:

   f'(x) = 9 * 5 * x^(9-1) = 45x^8

3. Next, substitute x = 2 into the derivative:

   f'(2) = 45 * (2^8)

4. Now, calculate 2^8:

   2^8 = 256

5. Finally, multiply:

   f'(2) = 45 * 256 = 11520

Therefore, the derivative of the function f(x) = 5x^9 at x = 2 is 11520.