Find the derivative of the function.

f(x) = e^x8 - 6

To find the derivative of the given function f(x) = e^(x^8 - 6), we'll use the chain rule.

Step 1: Identify the outer function and the inner function.
The outer function is e^x, while the inner function is x^8 - 6.

Step 2: Find the derivative of the outer function.
The derivative of e^x is simply e^x.

Step 3: Find the derivative of the inner function.
The derivative of x^8 is 8x^(8-1) = 8x^7, and the derivative of -6 is 0.

Step 4: Apply the chain rule.
The chain rule states that the derivative of the composition of two functions is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

Thus, the derivative of f(x) = e^(x^8 - 6) is:
f'(x) = e^(x^8 - 6) * (8x^7)

Therefore, the derivative of the function f(x) = e^x^8 - 6 is f'(x) = e^(x^8 - 6) * 8x^7.