Derivative of y=sinx+2x⁶

1. Differentiate $2 x^{6} + \sin{\left(x \right)}$ term by term:

   1. The derivative of sine is cosine:

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

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

      1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$

      So, the result is: $12 x^{5}$

   The result is: $12 x^{5} + \cos{\left(x \right)}$

The answer is:

$$12 x^{5} + \cos{\left(x \right)}$$