Derivative of y=2sinx-4x+3x^2-5

1. Differentiate $\left(3 x^{2} + \left(- 4 x + 2 \sin{\left(x \right)}\right)\right) - 5$ term by term:

   1. Differentiate $3 x^{2} + \left(- 4 x + 2 \sin{\left(x \right)}\right)$ term by term:

      1. Differentiate $- 4 x + 2 \sin{\left(x \right)}$ term by term:

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

            1. The derivative of sine is cosine:

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

            So, the result is: $2 \cos{\left(x \right)}$

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

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

            So, the result is: $-4$

         The result is: $2 \cos{\left(x \right)} - 4$

      2. 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: $6 x$

      The result is: $6 x + 2 \cos{\left(x \right)} - 4$

   2. The derivative of the constant $-5$ is zero.

   The result is: $6 x + 2 \cos{\left(x \right)} - 4$

The answer is:

$$6 x + 2 \cos{\left(x \right)} - 4$$