Derivative of y=x^5+7x+3

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

   1. Differentiate $x^{5} + 7 x$ term by term:

      1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$

      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: $7$

      The result is: $5 x^{4} + 7$

   2. The derivative of the constant $3$ is zero.

   The result is: $5 x^{4} + 7$

The answer is:

$$5 x^{4} + 7$$