Question

Find the derivative
f’ (2) if f(x) =3/(x+2)

Answer 1

Solving for the Derivative of a Function

Answer:

`f'(2) = -(3)/(16)\\`

Explanation:

Given:

`f(x) = (3)/(x +2)\\`

Recall:

`\frac{\text{d}}{\text{d}x}f(x) = f'(x)\\`

`\frac{\text{d}}{\text{d}x}((f(x))/(g(x))) = (f'(x)g(x) -f(x)g'(x))/(g(x)^2)\\`

If we want to solve for
`f'(2)`, we must first find how
`f'(x)` will be defined.

`f'(x) = \frac{\text{d}}{\text{d}x}f(x) \\ f'(x) = \frac{\text{d}}{\text{d}x}((3)/(x +2)) \\ f'(x) = (3' \cdot (x +2) -3 \cdot (x +2)')/((x +2)^2) \\ f'(x) = (0(x +2) -3(1))/((x +2)^2) \\ f'(x) = (-3)/((x +2)^2) \\ f'(x) = -(3)/((x +2)^2)`

Now we can evaluate
`f'(2)`.

`f'(2) = -(3)/((2 +2)^2) \\ f'(2) = -(3)/((4)^2) \\ f'(2) = -(3)/(16)`