Derivative of 2x^4+3x^3-7x+1

1. Differentiate $\left(- 7 x + \left(2 x^{4} + 3 x^{3}\right)\right) + 1$ term by term:

   1. Differentiate $- 7 x + \left(2 x^{4} + 3 x^{3}\right)$ term by term:

      1. Differentiate $2 x^{4} + 3 x^{3}$ 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: $x^{4}$ goes to $4 x^{3}$

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

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

            1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

            So, the result is: $9 x^{2}$

         The result is: $8 x^{3} + 9 x^{2}$

      2. 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: $-7$

      The result is: $8 x^{3} + 9 x^{2} - 7$

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

   The result is: $8 x^{3} + 9 x^{2} - 7$

The answer is:

$$8 x^{3} + 9 x^{2} - 7$$