Question

Find the derivative of f(x) = 3 divided by x at x = 1. (6 points)

Answer 1

For this case we have to by definition:

`\frac {d} {dx} (x ^ n) = nx ^ {n-1}`

So, if we have the following expression:

`f (x) = \frac {3} {x}\\f (x) = 3x^(-1)`

Deriving:

`\frac {df (x)} {dx} = - 1 (3) x ^ {-1-1} = - 3x ^ {-2} = - \frac {3} {x ^ 2}`

Evaluating at
`x = 1`:

`- \frac {3} {1 ^ 2} = - \frac {3} {1} = - 3`

Answer:

-3