Derivative of y=e^2x-lnx+6^x

1. Differentiate $6^{x} + \left(e^{2} x - \log{\left(x \right)}\right)$ term by term:

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

      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: $e^{2}$

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

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

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

      The result is: $e^{2} - \frac{1}{x}$

   2. $\frac{d}{d x} 6^{x} = 6^{x} \log{\left(6 \right)}$

   The result is: $6^{x} \log{\left(6 \right)} + e^{2} - \frac{1}{x}$

2. Now simplify:

   $$6^{x} \log{\left(6 \right)} + e^{2} - \frac{1}{x}$$

The answer is:

$$6^{x} \log{\left(6 \right)} + e^{2} - \frac{1}{x}$$