Derivative of e^sinx-2x

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

   1. Let $u = \sin{\left(x \right)}$.

   2. The derivative of $e^{u}$ is itself.

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(x \right)}$:

      1. The derivative of sine is cosine:

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

      The result of the chain rule is:

      $$e^{\sin{\left(x \right)}} \cos{\left(x \right)}$$

   4. 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: $-2$

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

The answer is:

$$e^{\sin{\left(x \right)}} \cos{\left(x \right)} - 2$$