Derivative It

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It looks like you’ve shared an expression and asked to find its derivative. To clarify, the expression in the image reads:

[

\lim_{x \to 0} \frac{\sqrt{1 - 8 \sin x} - 1}{x}

]

To find this limit, we can use techniques from calculus, including L’Hôpital’s Rule if the limit initially results in an indeterminate form like ( \frac{0}{0} ). Let’s proceed to evaluate this limit.

```
from sympy import symbols, sin, sqrt, limit
# Define the variable and expression
x = symbols('x')
expression = (sqrt(1 - 8 * sin(x)) - 1) / x
# Compute the limit as x approaches 0
lim_result = limit(expression, x, 0)
lim_result
```

The limit of the given expression as ( x ) approaches 0 is (-4). If you have any other questions or need further explanation, feel free to ask!