Derivative of sin(7^x)

1. Let $u = 7^{x}$.

2. The derivative of sine is cosine:

   $$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 7^{x}$:

   1. $\frac{d}{d x} 7^{x} = 7^{x} \log{\left(7 \right)}$

   The result of the chain rule is:

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

The answer is:

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