Derivative of f(x)=4sinx+5cosx

1. Differentiate $4 \sin{\left(x \right)} + 5 \cos{\left(x \right)}$ 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 sine is cosine:

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

      So, the result is: $4 \cos{\left(x \right)}$

   2. 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: $- 5 \sin{\left(x \right)}$

   The result is: $- 5 \sin{\left(x \right)} + 4 \cos{\left(x \right)}$

The answer is: