https://file.aiquickdraw.com/mathbot/file/17290509214735vzeaq8g.jpg

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.

Differentiate the following function: y = 5x^(-11)

Learn how to differentiate the function y = 5x^(-11) using the power rule. This problem covers key calculus concepts, including the application of the power rule in differentiation. Suitable for students in Grades 11-12.

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