Derivative of x^4-3x^2*7x

1. Differentiate $x^{4} - x 7 \cdot 3 x^{2}$ term by term:

   1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$

   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 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 $1$

            $g{\left(x \right)} = x^{2}$; to find $\frac{d}{d x} g{\left(x \right)}$:

            1. Apply the power rule: $x^{2}$ goes to $2 x$

            The result is: $3 x^{2}$

         So, the result is: $63 x^{2}$

      So, the result is: $- 63 x^{2}$

   The result is: $4 x^{3} - 63 x^{2}$

2. Now simplify:

   $$x^{2} \left(4 x - 63\right)$$

The answer is:

$$x^{2} \left(4 x - 63\right)$$