Derivative of 4/sqrx+3/x-2e^x

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

   1. Differentiate $\frac{4}{x^{2}} + \frac{3}{x}$ term by term:

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

         1. Let $u = x^{2}$.

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

         3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$:

            1. Apply the power rule: $x^{2}$ goes to $2 x$

            The result of the chain rule is:

            $$- \frac{2}{x^{3}}$$

         So, the result is: $- \frac{8}{x^{3}}$

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

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

         So, the result is: $- \frac{3}{x^{2}}$

      The result is: $- \frac{3}{x^{2}} - \frac{8}{x^{3}}$

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

      1. The derivative of $e^{x}$ is itself.

      So, the result is: $- 2 e^{x}$

   The result is: $- 2 e^{x} - \frac{3}{x^{2}} - \frac{8}{x^{3}}$

The answer is:

$$- 2 e^{x} - \frac{3}{x^{2}} - \frac{8}{x^{3}}$$