Derivatives of Polynomials

To differentiate polynomials you have to first identify the variable and constant terms in the equation. y = 6x^3 + 7x^2 + 4x + 2 The variable terms are 6x3, 7x^2, and 4x The constant term is 2. Then you multiply the coefficients of each variable term by the exponent. 6x^3 = 6 x 3 = 18 7x^2 = 7x 2 = 14 4x = 4 x 1 = 4 After this you would lower each exponent by one degree. 6x^3 = 6x^2 7x^2 = 7x^1 4x = 4 Next you replace the old coefficients and old exponents with their new counterparts. 6x^3 becomes 18x^2 7x^2 becomes 14x 4x becomes 4 The derivative of the polynomial y = 6x^3 + 7x^2 + 4x + 2 is y = 18x^2 + 14x + 4 Finally you would find the value of the new equation with a given "x" value. If the given "x" value is 2 y = 18x^2+14x+4 = 18 x 2^2 + 14x 2 + 4 = y = 72 + 28 + 4 = 104 The value of the equation at x = 2 is 104.

There are many steps to differentiating polynomials. The first step would be to idenify the variables and the constants. The second step is to multiply the coefficents of each variable by the exponet. The third step is to lower each exponet by one degree. To finsh differentiating polynomials you have to replace the old co-efficients with the new ones. Last step would be to use the given "x" value with the new

The first form of Power Rule was used by Bonaventura Cavalieri in the 17 century and was later improved by Newton and Leibniz who was both working individually. The power rule is used in calculus to differentiate functions.

An example of that would be X^2. This function is one of the more simpler ones because it is a nominal. The formula to find the derivative of X^2 is nX^n-1. This formula works for all types of function to find the derivative.

To solve X^2 we would use nX^n-1 to find its derivative. N is the exponent. The derivative of X^2 is 2X because The exponent would be moved down to in front of X and the exponent would be subtracted by 1.

A more complex function would be 3X^3 + 4X^2 + 9X + 10. Again we would use the formula nX^n-1. The derivative of 3X^3 + 4X^2 + 9X + 10 would be 9X^2 + 8X + 9 + 0 because 3X^3,The 3 would be multiplied by the number in front of the X and the exponent would be subtracted by 1, ,4X^2,The exponent would be multiplied by the number in front of the X and the exponent subtracted by 1, and same for 9X. The reason why 10 becomes zero because it has no exponents in it. and the exponent of 0 would equals to zero because anything to the 0 power would equal to 0.

Everything in the Power Rule will eventually become 0. This is because as we keep finding the derivative of the derivative the exponent will be subtracted by 1 and eventually it will hit 0.