Derivative of 2x*lnx-x*ln49

1. Differentiate $2 x \log{\left(x \right)} - x \log{\left(49 \right)}$ term by term:

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

      1. Apply the product rule:

         $$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$$

         $f{\left(x \right)} = x$; to find $\frac{d}{d x} f{\left(x \right)}$:

         1. Apply the power rule: $x$ goes to $1$

         $g{\left(x \right)} = \log{\left(x \right)}$; to find $\frac{d}{d x} g{\left(x \right)}$:

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

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

      So, the result is: $2 \log{\left(x \right)} + 2$

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

      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: $\log{\left(49 \right)}$

      So, the result is: $- \log{\left(49 \right)}$

   The result is: $2 \log{\left(x \right)} - \log{\left(49 \right)} + 2$

The answer is: