Derivative of y=9x^5+2sinx-10

1. Differentiate $\left(9 x^{5} + 2 \sin{\left(x \right)}\right) - 10$ term by term:

   1. Differentiate $9 x^{5} + 2 \sin{\left(x \right)}$ term by term:

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

         1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$

         So, the result is: $45 x^{4}$

      2. 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: $2 \cos{\left(x \right)}$

      The result is: $45 x^{4} + 2 \cos{\left(x \right)}$

   2. The derivative of the constant $-10$ is zero.

   The result is: $45 x^{4} + 2 \cos{\left(x \right)}$

The answer is:

$$45 x^{4} + 2 \cos{\left(x \right)}$$