Derivative of (√5)t+√7/t

1. Differentiate $\sqrt{5} t + \frac{\sqrt{7}}{t}$ 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: $t$ goes to $1$

      So, the result is: $\sqrt{5}$

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

      1. Apply the power rule: $\frac{1}{t}$ goes to $- \frac{1}{t^{2}}$

      So, the result is: $- \frac{\sqrt{7}}{t^{2}}$

   The result is: $\sqrt{5} - \frac{\sqrt{7}}{t^{2}}$

The answer is:

$$\sqrt{5} - \frac{\sqrt{7}}{t^{2}}$$