The function given in the image is:

$y = 5x^{-11}$

To differentiate this function, we will use the power rule for differentiation. The power rule states that for a function of the form $y = ax^n$, the derivative is given by:

$\frac{dy}{dx} = a \cdot n \cdot x^{n-1}$

Applying the power rule:

1. The coefficient $a = 5$,
2. The exponent $n = -11$.

Now, differentiate:

$y' = 5 \cdot (-11) \cdot x^{-11 - 1} = -55x^{-12}$

Thus, the derivative is:

$y' = -55x^{-12}$

Would you like a detailed explanation or any clarifications?

Here are five related questions for practice:

1. Differentiate $y = 3x^{-4}$.
2. What is the derivative of $y = 7x^5$?
3. How do you find the derivative of $y = x^{-2}$?
4. Differentiate $y = -6x^{3}$.
5. What is the derivative of $y = 4x^{-10}$?

Tip: The power rule is a quick method to differentiate terms where the variable $x$ is raised to a constant power.