Derivative of -0,1cos(10x)+20

1. Differentiate $20 - \frac{\cos{\left(10 x \right)}}{10}$ term by term:

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

      1. Let $u = 10 x$.

      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 $\frac{d}{d x} 10 x$:

         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: $10$

         The result of the chain rule is:

         $$- 10 \sin{\left(10 x \right)}$$

      So, the result is: $\sin{\left(10 x \right)}$

   2. The derivative of the constant $20$ is zero.

   The result is: $\sin{\left(10 x \right)}$

The answer is:

$$\sin{\left(10 x \right)}$$