Question

Find the derivative of f(x) = negative 9 divided by x at x = -8.

Answer 1

The derivative of f(x) = -9/x at x = -8 is found using the power rule for differentiation, resulting in f'(x) = 9x^-2. After simplifying and substituting x = -8, the derivative is calculated to be 9/64.

Step-by-step explanation:

To find the derivative of f(x) = -9/x at x = -8, we can use the power rule for differentiation. The given function is a negative constant multiplied by x raised to the power of -1. Using the power rule, which states that if f(x) = xn, then f'(x) = nxn-1, we can differentiate our function.

The derivative of f(x) = -9x-1 is f'(x) = -9(-1)x-1-1 = 9x-2. Evaluating this at x = -8 gives us f'(-8) = 9/(-8)2 = 9/64.

Therefore, the derivative of the function f(x) = -9/x at the point x = -8 is 9/64.

Answer 2

The derivative given in the question is
f(x) = - 9 /x
When x = -8, then
f(-8) = 9/8
The negative sign on the right hand side gets cancelled out. From the above deduction, it can be easily concluded that the answer is 9/8. I hope that this is the answer that you were looking for and the answer has actually come to your desired help.