The formula for finding the derivative of a polynomial function is to multiply each term by its exponent and then subtract 1 from the exponent. For example, the derivative of x^2 would be 2x, and the derivative of 2x^3 would be 6x^2.
To apply the power rule, you must first identify the terms in the polynomial function and their corresponding exponents. Then, multiply each term by its exponent and subtract 1 from the exponent. Finally, combine like terms to simplify the resulting expression.
The derivative of (x^2-6x+9)(2x^2-x+1) is 2x^4-14x^3+25x^2-12x+9.
To simplify the derivative of (x^2-6x+9)(2x^2-x+1), you must first expand the polynomial function to get 2x^4-14x^3+25x^2-12x+9. Then, combine like terms to get the simplified expression.
The derivative of a polynomial function represents the slope of the function at a given point. It can also be used to find the rate of change of the function, as well as the critical points and extrema of the function. This makes it a crucial tool in many areas of science and mathematics.