Derivative of 5*exp(-x)-sin(14*x)

1. Differentiate $- \sin{\left(14 x \right)} + 5 e^{- x}$ term by term:

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

      1. Let $u = - x$.

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

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

         1. 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: $-1$

         The result of the chain rule is:

         $$- e^{- x}$$

      So, the result is: $- 5 e^{- x}$

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

      1. Let $u = 14 x$.

      2. The derivative of sine is cosine:

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

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 14 x$:

         1. 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: $14$

         The result of the chain rule is:

         $$14 \cos{\left(14 x \right)}$$

      So, the result is: $- 14 \cos{\left(14 x \right)}$

   The result is: $- 14 \cos{\left(14 x \right)} - 5 e^{- x}$

The answer is:

$$- 14 \cos{\left(14 x \right)} - 5 e^{- x}$$