Derivative of (1/4)^x

1. Let $u = - x$.

2. $\frac{d}{d u} 4^{u} = 4^{u} \log{\left(4 \right)}$

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:

   $$- 4^{- x} \log{\left(4 \right)}$$

4. Now simplify:

   $$- 2 \cdot 4^{- x} \log{\left(2 \right)}$$

The answer is:

$$- 2 \cdot 4^{- x} \log{\left(2 \right)}$$