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.