Derivative of 5x^4+2x^3

1. Differentiate $5 x^{4} + 2 x^{3}$ term by term:

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

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

      So, the result is: $20 x^{3}$

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

      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

      So, the result is: $6 x^{2}$

   The result is: $20 x^{3} + 6 x^{2}$

2. Now simplify:

   $$x^{2} \cdot \left(20 x + 6\right)$$

The answer is:

$$x^{2} \cdot \left(20 x + 6\right)$$