Derivative of 4sqrt(x)+7x^2

1. Differentiate $4 \sqrt{x} + 7 x^{2}$ 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: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$

      So, the result is: $\frac{2}{\sqrt{x}}$

   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: $14 x$

   The result is: $14 x + \frac{2}{\sqrt{x}}$

The answer is:

$$14 x + \frac{2}{\sqrt{x}}$$