Derivative of y=sinx+3x³

1. Differentiate $3 x^{3} + \sin{\left(x \right)}$ 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: $x^{3}$ goes to $3 x^{2}$

      So, the result is: $9 x^{2}$

   The result is: $9 x^{2} + \cos{\left(x \right)}$

The answer is:

$$9 x^{2} + \cos{\left(x \right)}$$