Derivative of 7^(x/2)

1. Let $u = \frac{x}{2}$.

2. $\frac{d}{d u} 7^{u} = 7^{u} \log{\left(7 \right)}$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{x}{2}$:

   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: $\frac{1}{2}$

   The result of the chain rule is:

   $$\frac{7^{\frac{x}{2}} \log{\left(7 \right)}}{2}$$

4. Now simplify:

   $$\frac{7^{\frac{x}{2}} \log{\left(7 \right)}}{2}$$

The answer is:

$$\frac{7^{\frac{x}{2}} \log{\left(7 \right)}}{2}$$