Derivative of 3x-4x^(1/3)+2

1. Differentiate $\left(- 4 \sqrt[3]{x} + 3 x\right) + 2$ term by term:

   1. Differentiate $- 4 \sqrt[3]{x} + 3 x$ 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: $3$

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

         1. Apply the power rule: $\sqrt[3]{x}$ goes to $\frac{1}{3 x^{\frac{2}{3}}}$

         So, the result is: $- \frac{4}{3 x^{\frac{2}{3}}}$

      The result is: $3 - \frac{4}{3 x^{\frac{2}{3}}}$

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

   The result is: $3 - \frac{4}{3 x^{\frac{2}{3}}}$

The answer is:

$$3 - \frac{4}{3 x^{\frac{2}{3}}}$$