Find the derivative of the function.
f(x) = ex8 - 6
To find the derivative of the function f(x) = ex^8 - 6, we can use the power rule for differentiation.
The power rule states that if we have a function of the form f(x) = cx^n, where c is a constant and n is a real number, then the derivative of the function is given by f'(x) = cnx^(n-1).
In this case, f(x) = ex^8 - 6. The derivative with respect to x, f'(x), can be found by applying the power rule to each term in the function.
First, let's find the derivative of the term ex^8.
Using the power rule, the derivative of ex^8 with respect to x is given by:
(d/dx)(ex^8) = 8ex^(8-1) = 8ex^7.
Next, let's find the derivative of the constant term -6.
The derivative of a constant is always zero, so (d/dx)(-6) = 0.
Therefore, the derivative of the function f(x) = ex^8 - 6 is:
f'(x) = 8ex^7 - 0 = 8ex^7.
So, the derivative of f(x) is 8ex^7.