Question

Differentiate. y=5 x²-7 x+1

Answer 1

To differentiate the function y=5x²-7x+1, apply the power rule to each term. The derivative of the function, y'=dy/dx, is 10x - 7.

Step-by-step explanation:

The student has asked how to differentiate the function y=5x²-7x+1. To find the derivative of this function, we apply the basic rules of differentiation.

• The derivative of a constant is 0.
• The derivative of x to the power of a positive integer n is n times x to the power of (n-1).

The function y=5x²-7x+1 is a polynomial, and we can differentiate each term separately:

1. The derivative of 5x² is 2*5x or 10x.
2. The derivative of -7x is -7.
3. The derivative of the constant 1 is 0.

Therefore, the derivative of the function y with respect to x, denoted as y' or dy/dx, is 10x - 7.