Question

Find f'(x) for the given function.

f(x) = 5/3-x

Answer 1

The derivative is:

`f^(\prime)(x) = -(5)/(x^2-6x+9)`

Explanation:

We are given the following function:

`f(x) = (5)/(3-x)`

Derivative of a quotient:

Suppose we have a quotient:

`f(x) = (g(x))/(h(x))`

The derivative is:

`f^(\prime)(x) = (g^(\prime)(x)h(x) - h^(\prime)(x)g(x))/(h(x)^2)`

In this question:

Numerator
`g(x) = 5, g^(\prime)(x) = 0`

Denominator
`h(x) = 3 - x, h^(\prime)(x) = -1`

So

`f^(\prime)(x) = (0(3-x) - 5)/((3 - x)^2) = -(5)/(x^2-6x+9)`

The derivative is:

`f^(\prime)(x) = -(5)/(x^2-6x+9)`