Question

Find the derivative of 1/√s+2

Answer 1

Using the quotient rule, it is found that the derivative of the function is given as follows:

$f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}$

What is the derivative of a quotient?

Suppose a quotient function defined as follows:

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

Then, the derivative is given by:

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

In this problem, we have that:

• g(x) = 1.

• g'(x) = 0.

• $h(x) = \sqrt{s} + 2$.

• $h^{\prime}(x) = \frac{1}{2\sqrt{s}}$

Then, since g'(x) = 0, the derivative is given by:

$f^{\prime}(x) = -\frac{1}{2\sqrt{s}(\sqrt{s}+2)^2}$

More can be learned about the quotient rule at brainly.com/question/27072366

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