Derivative of y=2^x-log7x

1. Differentiate $2^{x} - \log{\left(7 x \right)}$ term by term:

   1. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Let $u = 7 x$.

      2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$.

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

         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: $7$

         The result of the chain rule is:

         $$\frac{1}{x}$$

      So, the result is: $- \frac{1}{x}$

   The result is: $2^{x} \log{\left(2 \right)} - \frac{1}{x}$

The answer is:

$$2^{x} \log{\left(2 \right)} - \frac{1}{x}$$