Using the quotient rule, it is found that the derivative of the function is given as follows:
[tex]f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}[/tex]
What is the derivative of a quotient?
Suppose a quotient function defined as follows:
[tex]f(x) = \frac{g(x)}{h(x)}[/tex]
Then, the derivative is given by:
[tex]f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}[/tex]
In this problem, we have that:
- [tex]h(x) = \sqrt{s} + 2[/tex].
- [tex]h^{\prime}(x) = \frac{1}{2\sqrt{s}}[/tex]
Then, since g'(x) = 0, the derivative is given by:
[tex]f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}[/tex]
More can be learned about the quotient rule at https://brainly.com/question/27072366
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