Derivative of y=ln^3√5x+4

1. Differentiate $x \log{\left(\sqrt{5} \right)}^{3} + 4$ 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: $x$ goes to $1$

      So, the result is: $\log{\left(\sqrt{5} \right)}^{3}$

   2. The derivative of the constant $4$ is zero.

   The result is: $\log{\left(\sqrt{5} \right)}^{3}$

2. Now simplify:

   $$\frac{\log{\left(5 \right)}^{3}}{8}$$

The answer is:

$$\frac{\log{\left(5 \right)}^{3}}{8}$$