Derivative of y=(log6x+sinx)

1. Differentiate $\log{\left(6 x \right)} + \sin{\left(x \right)}$ term by term:

   1. Let $u = 6 x$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 6 x$:

      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: $6$

      The result of the chain rule is:

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

   4. The derivative of sine is cosine:

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

   The result is: $\cos{\left(x \right)} + \frac{1}{x}$

The answer is: