Derivative of cos(ctg(3))-7*x^2

1. Differentiate $- 7 x^{2} + \cos{\left(\cot{\left(3 \right)} \right)}$ term by term:

   1. Let $u = \cot{\left(3 \right)}$.

   2. The derivative of cosine is negative sine:

      $$\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$$

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cot{\left(3 \right)}$:

      1. There are multiple ways to do this derivative.

         Method #1

         1. Rewrite the function to be differentiated:

            $$\cot{\left(3 \right)} = \frac{1}{\tan{\left(3 \right)}}$$

         2. The derivative of the constant $\frac{1}{\tan{\left(3 \right)}}$ is zero.

         Method #2

         1. Rewrite the function to be differentiated:

            $$\cot{\left(3 \right)} = \frac{\cos{\left(3 \right)}}{\sin{\left(3 \right)}}$$

         2. The derivative of the constant $\frac{\cos{\left(3 \right)}}{\sin{\left(3 \right)}}$ is zero.

      The result of the chain rule is:

      $$0$$

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

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

      So, the result is: $- 14 x$

   The result is: $- 14 x$

The answer is:

$$- 14 x$$