Derivative of y=sqrtxx-12x+27

1. Differentiate $\left(- 12 x + \sqrt{x x}\right) + 27$ term by term:

   1. Differentiate $- 12 x + \sqrt{x x}$ term by term:

      1. Let $u = x x$.

      2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$

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

         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 $1$

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

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

            The result is: $2 x$

         The result of the chain rule is:

         $$\frac{x}{\left|{x}\right|}$$

      4. 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: $-12$

      The result is: $\frac{x}{\left|{x}\right|} - 12$

   2. The derivative of the constant $27$ is zero.

   The result is: $\frac{x}{\left|{x}\right|} - 12$

The answer is:

$$\frac{x}{\left|{x}\right|} - 12$$