Derivative of (3x^2)-5/(x+1)

1. Differentiate $3 x^{2} - \frac{5}{x + 1}$ 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: $x^{2}$ goes to $2 x$

      So, the result is: $6 x$

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

      1. Let $u = x + 1$.

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

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 1\right)$:

         1. Differentiate $x + 1$ term by term:

            1. Apply the power rule: $x$ goes to $1$

            2. The derivative of the constant $1$ is zero.

            The result is: $1$

         The result of the chain rule is:

         $$- \frac{1}{\left(x + 1\right)^{2}}$$

      So, the result is: $\frac{5}{\left(x + 1\right)^{2}}$

   The result is: $6 x + \frac{5}{\left(x + 1\right)^{2}}$

2. Now simplify:

   $$6 x + \frac{5}{\left(x + 1\right)^{2}}$$

The answer is:

$$6 x + \frac{5}{\left(x + 1\right)^{2}}$$