Question

Differentiate the function. y = 2x² - 2x + 8x.

Answer 1

To differentiate the function y = 2x² - 2x + 8x, apply the power rule and the sum/difference rule of differentiation.

Step-by-step explanation:

To differentiate the function y = 2x² - 2x + 8x, you need to apply the power rule and the sum/difference rule of differentiation. Here are the steps:

1. Take the derivative of each term separately using the power rule: dy/dx = 4x - 2 + 8
2. Simplify the expression by combining like terms: dy/dx = 4x + 6
3. Differentiate each term separately. The derivative of 2x² is 4x, and the derivative of 6x is 6.
4. Combine the derivatives of each term to get the final result.
5. Therefore, the derivative of the function y = 2x² + 6x is dy/dx = 4x + 6.