Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Find the derivative of 1/√s+2

Sagot :

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:

  • g(x) = 1.
  • g'(x) = 0.
  • [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

#SPJ1