Question

Find the Derivative - d/dx y=4x^2-6x+1

Answer 1

The derivative of the function y = 4x^2 - 6x + 1 is found by applying the power rule to each term, resulting in dy/dx = 8x - 6, which represents the slope of the tangent line to the curve at any point x.

Step-by-step explanation:

To find the derivative of the function y = 4x^2 - 6x + 1, we will apply the basic differentiation rules such as the power rule. The power rule states that the derivative of x^n with respect to x is nx^(n-1).

1. Identify the function to differentiate, which is y = 4x^2 - 6x + 1.
2. Apply the power rule to each term: the derivative of 4x^2 is 8x, and the derivative of -6x is -6.
3. The constant term 1 has a derivative of 0 because the derivative of any constant is 0.
4. Combine the derivatives of the individual terms to get the final derivative dy/dx = 8x - 6.

In conclusion, the derivative of y = 4x^2 - 6x + 1 with respect to x is dy/dx = 8x - 6. This represents the slope of the tangent line to the curve at any point x.