Given the function $f(x)=-x^{3}-18 x^{2}-81 x$, determine all interfals on which $f^{\prime}$ is decreasing.

Step 1 ：First, we need to find the derivative of the function $f(x)$. The function is given by $f(x) = -x^3 - 18x^2 - 81x$. Using the power rule, we find the derivative $f'(x)$:

Step 2 ：f'(x) = \(-3x^2 - 36x - 81\)

Step 3 ：Now, we need to find the intervals where $f''(x)$ is negative, as this indicates that $f'(x)$ is decreasing. To do this, we first find the second derivative $f''(x)$:

Step 4 ：f''(x) = \(-6x - 36\)

Step 5 ：Now, we need to find the intervals where $f''(x)$ is negative. To do this, we solve the inequality $f''(x) < 0$:

Step 6 ：\(-6x - 36 < 0\)

Step 7 ：Divide both sides by -6:

Step 8 ：\(x + 6 > 0\)

Step 9 ：So, the inequality is satisfied when $x > -6$. Therefore, the interval on which $f'(x)$ is decreasing is:

Step 10 ：\boxed{(-6, \infty)}