Derivative of y=2x^5-4x^3+5x-6

1. Differentiate $2 x^{5} - 4 x^{3} + 5 x - 6$ 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: $x^{5}$ goes to $5 x^{4}$

      So, the result is: $10 x^{4}$

   2. 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: $x^{3}$ goes to $3 x^{2}$

         So, the result is: $12 x^{2}$

      So, the result is: $- 12 x^{2}$

   3. 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: $5$

   4. The derivative of the constant $\left(-1\right) 6$ is zero.

   The result is: $10 x^{4} - 12 x^{2} + 5$

The answer is:

$$10 x^{4} - 12 x^{2} + 5$$