Derivative of 3^-x

1. Let $u = - x$.

2. $\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}$

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:

   $$- 3^{- x} \log{\left(3 \right)}$$

The answer is:

$$- 3^{- x} \log{\left(3 \right)}$$