Derivative of sinx-3x⁵+5

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

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

         So, the result is: $- 15 x^{4}$

      The result is: $- 15 x^{4} + \cos{\left(x \right)}$

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

   The result is: $- 15 x^{4} + \cos{\left(x \right)}$

The answer is:

$$- 15 x^{4} + \cos{\left(x \right)}$$