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

1. Differentiate $7 x^{7} + 3 x^{2} - 4 x - 1$ 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: $x^{7}$ goes to $7 x^{6}$

      So, the result is: $49 x^{6}$

   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: $6 x$

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

      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: $4$

      So, the result is: $-4$

   4. The derivative of the constant $\left(-1\right) 1$ is zero.

   The result is: $49 x^{6} + 6 x - 4$

The answer is:

$$49 x^{6} + 6 x - 4$$