Given the function f(x), the slope is evaluated by differentiating the f(x) function with respect to x.
Thus,

Given a function f(x) as
![f(x)\text{ = }\frac{4}{\sqrt[]{x+5}}](https://img.qammunity.org/2023/formulas/mathematics/college/meuqr27i84cj70hg91t7u0zrcb8dv9jgcx.png)
Step 1:
Differentiate the f(x) function with respect to x.
![\begin{gathered} f(x)\text{ = }\frac{4}{\sqrt[]{x+5}}\text{ can also be written as} \\ f(x)\text{ = }4(x+5)^{-(1)/(2)} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/i08e6gtf5gza1heyt6zqf4es8s8j289x8u.png)
differentiating the f(x) function, we have

Step 2:
Evaluate the slope at the point (-1, 1).
The slope at the point (-1, 1) is evaluated by substituting the values of x and y into the f'(x) function.
Thus,

Hence, the slope of the function at the point (-1, 1) is
