Derivative of с*(x*lnx-x)+c

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

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

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

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

         2. 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: $-1$

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

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

   2. The derivative of the constant $c$ is zero.

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

The answer is: