Derivative of y=inx+8lgx

1. Differentiate $\log{\left(x \right)} + 8 \log{\left(x \right)}$ term by term:

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

   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: $\frac{8}{x}$

   The result is: $\frac{9}{x}$

The answer is:

$$\frac{9}{x}$$