Question

Find the derivative of f(x) = negative 9 divided by x at x = -4

Answer 1

The derivative of f'(x) = -9/x when x = 4 is 9/16.

Explanation:

We are to find the derivative of
`f(x) = (-9)/(x)` and
`x= -4`

`f(x) = (-9)/(x) = -9x^(-1)`

`f'(x) = [f(x)]'`

`f'(x) = (-9x)^(-1)`

We know that,

`(x^n)' = nx^(n-1) where n is a constant`

So,
`f'(x) = -9(-1)x^(-1-1)`

`f'(x) = 9x^(-2)  = (9)/(x^2)`

Therefore when
`x=-4`,

`f'(-4)= (9)/(-4^2)`
`= (9)/(16)`

Therefore, the derivative of
`f'(x)= (-9)/(x)` when
`x= -4` is 9/16.

Answer 2

Answer: 9/16

Please, see the attached file.

Thanks.