To find the derivative \( \frac{d}{dx} \) of the function \( f(x) = x^3 - 11x^2 + 7x + 6 \), we will apply the power rule, which states:

\[
\frac{d}{dx}(x^n) = n x^{n-1}
\]

### Steps:
1. The derivative of \( x^3 \) is \( 3x^2 \).
2. The derivative of \( -11x^2 \) is \( -22x \).
3. The derivative of \( 7x \) is \( 7 \).
4. The derivative of the constant \( 6 \) is \( 0 \).

### Therefore, the derivative is:
\[
\frac{d}{dx}(x^3 - 11x^2 + 7x + 6) = 3x^2 - 22x + 7
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the derivative of a product of functions (product rule)?
2. What is the second derivative of \( f(x) = x^3 - 11x^2 + 7x + 6 \)?
3. How can you use the derivative to find critical points of a function?
4. What is the meaning of the derivative in the context of graphing a function?
5. How do you find the derivative of a quotient of functions (quotient rule)?

**Tip:** Always simplify the terms of a polynomial before finding its derivative.

Learn how to find the derivative of the polynomial function f(x) = x^3 - 11x^2 + 7x + 6. This solution demonstrates the use of the power rule to compute the derivative step-by-step. Suitable for students in Grades 10-12 studying calculus.

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