Question

Find f'(x) for the given function. f(x) = 5/3-x

Answer 1

Answer:

The derivative is:

$f^{\prime}(x) = -\frac{5}{x^2-6x+9}$

Step-by-step explanation:

We are given the following function:

$f(x) = \frac{5}{3-x}$

Derivative of a quotient:

Suppose we have a quotient:

$f(x) = \frac{g(x)}{h(x)}$

The derivative is:

$f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}$

In this question:

Numerator $g(x) = 5, g^{\prime}(x) = 0$

Denominator $h(x) = 3 - x, h^{\prime}(x) = -1$

So

$f^{\prime}(x) = \frac{0(3-x) - 5}{(3 - x)^2} = -\frac{5}{x^2-6x+9}$

The derivative is:

$f^{\prime}(x) = -\frac{5}{x^2-6x+9}$