Derivative of y=5x^4-3x^2+7

1. Differentiate $\left(5 x^{4} - 3 x^{2}\right) + 7$ term by term:

   1. Differentiate $5 x^{4} - 3 x^{2}$ 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: $x^{2}$ goes to $2 x$

         So, the result is: $- 6 x$

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

   2. The derivative of the constant $7$ is zero.

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

The answer is:

$$20 x^{3} - 6 x$$