Derivative of y'''=e^(5*x)-cosx

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

   1. Let $u = 5 x$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$:

      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: $5$

      The result of the chain rule is:

      $$5 e^{5 x}$$

   4. 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: $\sin{\left(x \right)}$

   The result is: $5 e^{5 x} + \sin{\left(x \right)}$

The answer is:

$$5 e^{5 x} + \sin{\left(x \right)}$$