Derivative of y=e^(6x)-11x^3

1. Differentiate $- 11 x^{3} + e^{6 x}$ term by term:

   1. Let $u = 6 x$.

   2. The derivative of $e^{u}$ is itself.

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 6 x$:

      1. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $6$

      The result of the chain rule is:

      $$6 e^{6 x}$$

   4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

      So, the result is: $- 33 x^{2}$

   The result is: $- 33 x^{2} + 6 e^{6 x}$

The answer is:

$$- 33 x^{2} + 6 e^{6 x}$$