Derivative of 62*cos(x)+65*x+45

1. Differentiate $\left(65 x + 62 \cos{\left(x \right)}\right) + 45$ term by term:

   1. Differentiate $65 x + 62 \cos{\left(x \right)}$ 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 cosine is negative sine:

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

         So, the result is: $- 62 \sin{\left(x \right)}$

      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: $65$

      The result is: $65 - 62 \sin{\left(x \right)}$

   2. The derivative of the constant $45$ is zero.

   The result is: $65 - 62 \sin{\left(x \right)}$

The answer is:

$$65 - 62 \sin{\left(x \right)}$$