Derivative of y=x^4-e^-x

1. Differentiate $x^{4} - e^{- x}$ term by term:

   1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$

   2. 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: $e^{- x}$

   The result is: $4 x^{3} + e^{- x}$

The answer is:

$$4 x^{3} + e^{- x}$$